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Published online by Cambridge University Press:  05 February 2015

Robert Fefferman
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University of Chicago
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Trigonometric Series , pp. 728 - 744
Publisher: Cambridge University Press
Print publication year: 2003

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References

Akhieser, N., Lectures on the theory of approximation (in Russian) (Moscow, 1947), pp. 1-307; English translation, Theory of Approximation (New York, 1956), pp. 1-307; German translation, Vorlesungen über Approximationstheorie (Berlin, 1953), pp. 1-309.
Banach, S., Opérations linéaires, Monografje Matematyczne (Warsaw, 1932), pp. vii + 254.
Boas, R. P., Entire functions (New York, 1954), pp. 1-276.
Bochner, S., Vorlesungen über Fouriersche Integrale (Leipzig, 1932), pp. 1-227.
Burkhaedt, H., Trigonometrische Reihen und Integrale (bis etwa 1850), Enz. d. Math. Wiss. II, A 12, 819-1354. Trigonometrische Interpolation, Enz. d. Math. Wiss. n, A 9a, 642-93.
Chandrasekharan, K. and Minakshisundaram, S., Typical means (Oxford, 1952), pp. 1-139.
Denjoy, A., Calcul des coefficients d'unes erie trigonometrique, four parts (Paris, 19411949), pp. 1-701.
Evans, G. C., The logarithmic potential, American Math. Soc. Coll. Publ. VT (1927), 1-150.
Grenander, U. and Szego, G., Toeplitz forms and their applications (Berkeley, Los Angeles. 1958), vii+ 245.
Hardy, G. H., Divergent Series (Oxford, 1949), pp. xiv + 396.
Hardy, G. H., Littlewood, J. E. and P6LYA, G., Inequalities (second edition) (Cambridge, 1952), pp. xii + 324.
Hardy, G. H. and Rogosinski, W. W., Fourier Series, Cambridge Tracts, no. 38 (1950), 1-100.
Hilb, E. and Riesz, M., Neuere Untersuchungen über trigonometrische Reihen, Enz. d. Math. Wiss. II, C 10, 1189-1228.
Hille, E., Walsh, J. L. and Shohat, J. A., A bibliography on orthogonal polynomials, Bull, of the Nat. Research Council, no. 103, Nat. Acad, of Sciences, Washington, 1940.
Jackson, D., The theory of approximation, American Math. Soc. Coll. Publ., XI, 1930, 1-178.
Jeffery, R. L., Trigonometric series, Canadian Math. Congress (Toronto, 1956), pp. 1-39.
Kaczmarz, S. and Steinhaus, H., Theorie der Orthogonalreihen, Monografje Matematyczne (Warsaw, 1935), pp. vi + 294.
Lebesgue, H., Lecons sur les series trigonom Uriques (Paris, 1906), pp. 1-128.
Levinson, N., Gap and density theorems, American Math. Soc. Coll. Publ. XXVI, 1940, viii + 246.
Littlewood, J. E., Lectures on the theory of functions (Oxford, 1944), pp. 1-243.
Mandelbrojt, S., Séries de Fourier et classes quasi-analytiques de fonctions (Paris, 1935), pp. viii + 156.
Nevanlinna, R., Eindeutige analytische Funktionen, 2nd edition (Springer, 1953), pp. 1-379.
Paley, R. E. A. C. and Wiener, N., Fourier transforms in the complex domain, American Math. Soc. Coll. Publ. XIX, 1934, 1-184.
Plessner, A., Trigonometrische Reihen, in Pascal's Repertorium d. höheren Analysis (I, 3), 1325–96.
Rado, T., Subharmonic functions, Ergebnisse d. Mathematik (Berlin, 1937), pp. 1-56.
Riesz, F. and Sz. B., Nagy, Leçons d'analyse fonctionnelle (Budapest, 1952), pp. viii + 448.
Schwartz, L., Théorie des distributions, vol. I (2nd edition), Actualités Scientifiques et Industrielles, no. 1245; vol. II, Theorie des distributions, no. 1122.
Szegö, G., Orthogonal polynomials, American Math. Soc. Coll. Publ. XXIII, 1939, vii + 401.
De La Vallée-Poussin, CH. J., Lecons sur Vapproximation des fonctions d'une variable réelle (Paris, 1919), pp. vi + 150.
Tonelli, L., Serie trigonometriche (Bologna, 1928), pp. viii + 526.
Wiener, N., The Fourier Integral and certain of its applications (Cambridge, 1933), pp. xi + 201.
[1] Akhieser, N. and Krein, M., On the best approximation of periodic functions by trigonometric sums (in Russian), Doklady, 15 (1937), 107–11.Google Scholar
[1] Agnew, R. P., Rogosinski-Bernstein trigonometric summability methods and modified arithmetic means, Ann. Math. 56 (1952), 53–79.Google Scholar
[1] Alexits, G., Sur l'ordre de grandeur de l'approximation d'une fonction par les moyennes de sa série de Fourier, Mat. Fiz. Lapok, 48 (1941), 410–22.Google Scholar
[2] Alexits, G., Über eine Hadamardsche Fragestellung, M.Z. 30 (1929), 43–6.Google Scholar
[1] Aliančić, S., Bojanić, R. and Tomić, JVL, Sur l'intégrabilité de certaines séries trigonométriques, Publ. Inst. Math. Acad. Serbe, 8 (1955), 67–84.Google Scholar
[2] Aliančić, S., Bojanić, R. and Tomić, JVL, Sur le comportement asymptotique au voisinage de zero des series trigonometriques de sinus a coefficients mononotes, ibid. 10 (1956), 101–20.Google Scholar
[1] Arbault, J., Sur l'ensemble de convergence absolue d'une serie trigonom∧trique, B.S.M.F. 80 (1952), 253–317.Google Scholar
[1] Bagemihl, F. and Seidel, W., Some boundary properties of analytic functions, M.Z. 61 (1954), 186–99.Google Scholar
[1] Banach, S., Uber eine Eigenschaft der lakunaren trigonometrischen Reihen, S.M. 2 (1930), 207–20.Google Scholar
[1] Banach, S. and Steinhaus, H., Sur le principe de condensation de singularity, F.M. 9 (1927), 50–61.Google Scholar
[1] Bary, N., Generalization of inequalities of S. N. Bernstein and A. A. Markov (in Russian), Izvestia, 18 (1954), 159–76.Google Scholar
[2] Bary, N., Sur l'unicité du développement trigonométrique, F.M. 9 (1927), 62–118.Google Scholar
[3] Bary, N., The uniqueness problem of the representation of functions by trigonometric series (in Russian), Uspekhi Matematičeskich Nauk, 4 (1949), no. 3, 3-68; English translation, American Math. Soc. no. 52 (New York, 1951), pp. 1-89.Google Scholar
[4] Bary, N., Sur l'unicité du développement trigonométrique, C.R. 177 (1923), 1195–7.Google Scholar
[5] Bary, N., Primitive functions and trigonometric series (in Russian), Sbornik, 31 (1952), 687–702.Google Scholar
[1] Bary, N. and Stečkin, S. B., Best approximation and differential properties of two conjugate functions (in Russian), Trudy Moskovskogo Matematičeskogo Obščestva, 5 (1956), 483–522.Google Scholar
[1] Bergman, S. and Marcinkiewicz, J., Sur les fonctions analytiques de deux variables complexes, F.M. 33 (1939), 75–94.Google Scholar
[1] Bernstein, S., Sur l'ordre de la meilleure approximation des fonctions continues par des polynômes de degré donnéMém. Acad. Roy. Belgique, 2me série, 4 (1912), 1–104.Google Scholar
[2] Bernstein, S., Bernstein, S., Sur la convergence absolue des séries trigonométriques, C.R. 158 (1914), 1661–4.Google Scholar
[3] Bernstein, S., Sur la convergence absolue des séries trigonométriques (in Russian), Comm. Soc. Math. Kharkov, 2me serie, 14 (1914), 139–44.Google Scholar
[4] Bernstein, S., Sur un procédé de sommation des séries trigonométriques, C.R. 191 (1930), 976–9.Google Scholar
[5] Bernstein, S., Sur une modification de la formule d'interpolation de Lagrange, Comm. de la Soc. Math, de Kharkov, 5 (1931), 49–57.Google Scholar
[6] Bernstein, S., Sur une classe de fbrmules d'interpolation, Izvestia, no. 9 (1931), pp. 1151–61.Google Scholar
[1] Bers, L., Bounded analytic functions of two complex variables, A.J.M. 64 (1942), 514–29.Google Scholar
[1] Besicovitch, A. S., Sur la nature des fonctions à carré sommable et des ensembles mesurables, F.M. 4 (1923), 172–95.Google Scholar
[2] Besicovitch, A. S., On a general metric property of summable functions, J.L.M.S. 1 (1926), 120–8.Google Scholar
[1] Beubling, A., Sur les intégrates de Fourier absolument convergentes, Neuvième Congrès des mathématiciens scandinaves (Helsingfors, 1938), pp. 345–66.
[2] Beurling, A., Etude sur un problème de majoration, Diss. (Uppsala, 1933), pp. 1-109.
[3] Beurling, A., Sur les ensembles exceptionnels, A.M. 72 (1940), 1–13.Google Scholar
[1] Billik, M., Orlicz spaces (M.A. thesis submitted at the Mass. Inst, of Technology), 1957.
[1] Birnbaum, Z. and Orlicz, W., Über die Verallgemeinerung des Begriffes der zueinander konjugierten Potenzen, S.M. 3 (1931), 1–67.Google Scholar
[1] Boas, R. P., Integrability of trigonometric series, (I) Duke J. 18 (1951), 787–93; (II) M.Z. 55 (1952), 183–6; (III) Q.J. 3 (1952), 217–21.Google Scholar
[1] Boas, R. P. and Bochner, S., On a theorem of M. Riesz for Fourier series, J.L.M.S. 14 (1939), 62–73.Google Scholar
[1] Bochner, S., Über Faktorenfolgen für Fouriersche Reihen, A.S. 4 (1929/, 125–9.Google Scholar
[2] Bochner, S., Boundary values of analytic functions in several variables and almost periodic functions, Ann. Math. 45 (1944), 708–22.Google Scholar
[3] Bochner, S., Summation of multiple Fourier series by spherical means, T.A.M.S. 40 (1936), 175–207.Google Scholar
[1] Bohr, H., Über einen Satz von J. Pál, A.S. 7 (1935), 129–35.Google Scholar
[1] Boks, T. J., Sur le rapport entre les méthodes d'intégration de Riemann et de Lebesgue, R.P. 45 (1921), 211–64.Google Scholar
[1] Borgen, S., Über (C, 1) Summierbarkeit von Reihen orthogonaler Funktionen, M.A. 98 (1928), 125–50.Google Scholar
[1] Bosanquet, L. S., Note on differentiated Fourier series, Q.J. 10 (1939), 67–74.Google Scholar
[2] Bosanquet, L. S., J On the summability of Fourier series, P.L.M.S. 31 (1930), 144–64.Google Scholar
[1] Broman, A., On two classes of trigonometrical series, Diss. (Uppsala, 1947), pp. 1-51.
Bruschi, M. and Cotlar, M., seeCotlar, M. and Bruschi, M.Burkill, J. C., [1] On the differentiability of multiple integrals, J.L.M.S. 26 (1951), 244–9.Google Scholar
[1] Calderón, A. P., On theorems of M. Riesz and Zygmund, Proc.A.M.S. 1 (1950), 533–5.Google Scholar
[2] Calderón, A. P., On the behaviour of harmonic functions on the boundary, T.A.M.S. 68 (1950), 47–54.Google Scholar
[3] Calderón, A. P., On a theorem of Marcinkiewicz and Zygmund, T.A.M.S.55-61.
[1] Calderón, A. P., González-Domínguez, A. and Zygmund, A., Nota sobre los valores limites de funciones analiticas, Revista de la Union Matemdtica Argentina, 14 (1949), 16–19.Google Scholar
[1] Calderón, A. P. and Zygmund, A., On t he theorem of Hausdorff-Young and its extensions, Ann. Math. Studies, 25 (1950), 166–88.Google Scholar
[2] Calderón, A. P. and Zygmund, A., Note on the boundary values of functions of several complex variables, Ann. Math. Studies, 25 (1950) 144–65.Google Scholar
[3] Calderón, A. P. and Zygmund, A., A note on the interpolation of sublinear operations, A.J.M. 78 (1956), 282–8.Google Scholar
[4] Calderón, A. P. and Zygmund, A., A note on the interpolation of linear operations, S.M. 12 (1951), 194–204.Google Scholar
[5] Calderón, A. P. and Zygmund, A., On singular integrals, A.M. 88 (1952), 85–139.Google Scholar
[1] Cantor, G., Über die Ausdehnung eines Satzes aus der Theorie der trigonometrischen Reihen, M.A. 5 (1872), 123–32.Google Scholar
[1] Carathéodory, C., Über die Variabilitätsbereich der Koeffizienten von Potenzreihen die gegebene Werte nicht annehmen, M.A. 64 (1907), 95–115.Google Scholar
[2] Carathéodory, C., Über die Fouriersche Koeffizienten monotoner Funktionen, Sitzungsberichte d. Preuss. Akad. der Wiss. 1920, pp. 559–73.
[1] Carleman, T., Sur les équations intégrates singulières à noyau réel et symétrique, Uppsala Universitets Årsskrift, 1923, pp. 1-228.
[2] Carleman, T., Über die Fourierkoeffizienten einer stetigen Funktion, A.M. 41 (1918), 377–84.Google Scholar
[3] Carleman, T., A theorem concerning Fourier Series, P.L.M.S. 21 (1923), 483–92.Google Scholar
[1] Carleson, L., Sets of uniqueness for functions regular in the unit circle, A.M. 87 (1952), 325–45.Google Scholar
[1] Cartwright, M., On analytic functions regular in the unit circle, Q.J. 4 (1933), 246–57.Google Scholar
Cartwright, M. and Collingwood, E. F., seeCollingwood, E. F. and Cartwright, M.Chaundy, T. W. and Jolliffe, A. E., [1] The uniform convergence of a certain class of trigonometrical series, P.L.M.S. 15 (1916), 214–16.Google Scholar
[1] Collingwood, E. F. and Cartwright, M., Boundary theorems for a function regular in the unit circle, A.M. 87 (1952), 83–146.Google Scholar
[1] Van Der Corput, J. G., Zahlentheoretische Abschatzungen, M.A. 84 (1921), 53–79.Google Scholar
[1] Cotlar, M. and Bruschi, M., On the convexity theorems of Riesz-Thorin and Marcinkiewicz, Revista, Universidad Nacional de la Plata, Publicaciones de la Facultad de Ciencias Fisicomatematicas, 5 (1956), 162–72.Google Scholar
[1] Cramer, H., Etudes sur la sommation des series de Fourier, Arkiv for Matematik, Astronomi och Fysik, 13 (1919), No. 20, 1-21.Google Scholar
[1] Denjoy, A., Sur l'absolue convergence des séries trigonométriques, C.R. 155 (1912), 135–6.Google Scholar
[2] Denjoy, A., Sur les ensembles parfaits présentant le caractère (A), Acc. Lincei, 29 2 (1920), 316–18.Google Scholar
[3] Denjoy, A., Sur l'integration riemannienne, C.R. 169 (1919), 219–21.Google Scholar
[1] Dieudonné, J. M., Sur les fonctions univalentes, C.R. 192 (1931), 1148–50.Google Scholar
[1] Doob, J. L., The boundary values of analytic functions, T.A.M.S. 34 (1932), 153–70.Google Scholar
[1] Edmonds, S., The Parseval formula for monotonic functions, Part I, Proc. Camb. Phil. Soc. 43 (1947), 289–306; Parts II and I I I, ibid. 46 (1950), 231–48, 249–67.Google Scholar
[1] Erdos, P., On the convergence of trigonometric series, J. Math. Phys. 22 (1943), 37–9.Google Scholar
[2] Erdos, P., Corrections to two of my papers, Ann. Math. 44 (1943), 647–51.Google Scholar
[3] Erdos, P., Some theorems and remarks on interpolation, A.S. 12 (1950), 11–17.Google Scholar
[4] Erdos, P., On a family of symmetric Bernoulli convolutions, A.J.M. 61 (1939), 974–6.Google Scholar
[1] Erdos, P. and Feldheim, E., Sur le mode de convergence dans l'interpolation de Lagrange, C.R. 203 (1936), 913–15.Google Scholar
[1] Erdos, P. and Gal, I., Law of the iterated logarithm, Indagationes Math. 17 (1955), 65–84.Google Scholar
[1] Erdos, P. and Turan, P., On interpolation, (I) Quadrature and mean convergence in the Lagrange interpolation, Ann. Math. 38 (1937), 142–55; (II) On the distribution of the fundamental points of Lagrange and Hermite interpolation, ibid. 39 (1938), 703–24; (III) Interpolatory theory of polynomials, ibid. 41 (1940), 510–53.Google Scholar
[1] Faber, G., Über das Verhalten analytischer Funktionen an Verzweigungsstellen, Miinchener Sitzungsberichte, 1917, pp. 263–84.
[2] Über stetige Funktionen, II, M.A. 69 (1910), 372–443.
[3] Über die interpolatorische Darstellung stetiger Funktionen, Jahresbericht d. Deutschett Math. Vereinigung, 23 (1914), 192–210.
[1] Fatou, P., Séries trigonométriques et séries de Taylor, A.M. 30 (1906), 335–400.Google Scholar
[2] Sur la convergence absolue des séries trigonométriques, B.S.M.F. 41 (1913), 47–53.
[1] Favard, J., Sur les meilleurs procédés d'approximation, B.S.M. 61 (1937), 209–24, 243–56.Google Scholar
[1] Fejér, L., Lebesguesche Konstanten und divergente Fourier-reihen, J.f.M. 139 (1910), 22–53.Google Scholar
[2] Fejer, L., Über die Bestimmung des Sprunges einer Funktion aus ihrer Fourierreihe, J.f.M. 142 (1913), 165–8.Google Scholar
[3] Fejer, L., Untersuchungen über Fouriersche Reihen, M.A. 58 (1904), 501–69.Google Scholar
[4] Fejer, L., Neue Eigenschaften der Mittelwerte bei den Fourierreihen, J.L.M.S. 8 (1933), 53–62.Google Scholar
[5] Fejer, L., Über gewisse durch die Fouriersche und Laplacesche Reihe definierte Mittelkurven und Mittelflächen, R.P. 38 (1914), 79–97.Google Scholar
[6] Fejer, L., Über die positivität von Summen die nach trigonometrischen und Legendreschen Funktionen fortschreiten, A.S. 2 (1925), 75–86.Google Scholar
[7] Fejer, L., Über Potenzreichen deren Summe im abgeschlossenen Konvergenzkreise überall stetig ist, Münchener Sitzungsberichte, 1917, pp. 33-50.
[8] Fejer, L., Sur les singularités de la série de Fourier des fonctions continues, A.E.N.S. 28 (1911), 63–103.Google Scholar
[9] Fejer, L., Über konjugierte trigonometrische Reihen, J.f.M. 144 (1913), 48–56.Google Scholar
[10] Fejer, L., Über gewisse Minimumprobleme der Funktionentheorie, M.A. 97 (1926), 104–23.Google Scholar
[11] Fejer, L., Trigonometrische Reihen und Potenzreihen mit mehrfach monotoner Koeffizientenfolge, T.A.M.S. 39 (1936), 18–59.Google Scholar
[12] Fejer, L., La convergence sur son cercle de convergence d'une série de puissances effectuant une representation conforme du cercle sur le plan simple, C.R. 156 (1913), 46–9.Google Scholar
[13] Fejer, L., Die Abschätzungen eines Polynomes in einem Intervalle, M.Z. 32 (1930), 426–57.Google Scholar
[1] Fejèr, L. and Riesz, F., Über einige Funktionentheoretische Ungleichungen, M.Z. 11 (1921), 305–14.Google Scholar
[1] Fekete, M., Über die Faktorenfolgen welche die ‘Klasse’ einer Fourierschen Reihe unverandert lassen, A.S. 1 (1923), 148–66.Google Scholar
[1] Feldheim, E., Théorie de la convergence des procédés d'interpolation et de quadrature mecanique, Mémorial des Sciences Math. 95 (1939), 1–90.Google Scholar
[1] Ferrand, J. and Fortet, R., Sur des suites arithmétiques équiréparties, C.R. 224 (1947), 516–18.Google Scholar
[1] Fichtenholz, G., Sur l'integrale de Poisson et quelques questions qui s'y rattachent, F.M. 13 (1929), 1–33.Google Scholar
[1] Fine, N., On the Walsh functions, T.A.M.S. 65 (1949), 372–414.Google Scholar
[2] Fine, N., Cesàro summability of Walsh-Fourier séries, Proc. Nat. Acad. U.S.A. 41 (1955), 588–91.Google Scholar
[1] Fischer, E., Sur la convergence en moyenne, C.R. 144 (1907), 1022–4.Google Scholar
[1] Flett, T. M., Some remarks on a maximal theorem of Hardy and Littlewood, Q.J. 6 (1955), 275–82.Google Scholar
[2] Flett, T. M., On some theorems of Littlewood and Paley, J.L.M.S. 31 (1956), 336–44.Google Scholar
[1] Frostman, O., Potentiel d'équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions, Comm. of the Math. Seminar of the U. of Lund, 3, 1-118.
[1] Gabriel, R. M., The rearrangement of positive Fourier coefficients, P.L.M.S. 33 (1932), 32–51.Google Scholar
[2] Gabriel, R. M., A star inequality for harmonic functions, P.L.M.S. 34 (1932), 305–13.Google Scholar
[1] Gage, W. H. and James, R. D., A generalized integral, Proc. Roy. Soc. Canada, 40 (1946), III, 25-36.Google Scholar
[1] Gattegno, C. and Ostrowski, A., Représentation conforme à la frontière, (I) Domaines généraux, Mémorial d. Sci. Math. 109 (1949), 1–58; (II) Domaines particuliers, Memorial d. Sci. Math. 110 (1949), 1–56.Google Scholar
[1] Geiringer, H., Trigonometrische Doppelreihen, M.f.M. 29 (1918), 65–144.Google Scholar
[1] Gergen, J. J., Convergence and summability criteria for Fourier séries, Q.J. 1 (1930), 252–75.Google Scholar
[1] Gosselin, R., On the convergence behavior of trigonometric interpolating polynomials, Pacific J. Math. 5 (1955), 915–22.Google Scholar
[1] Gbonwall, T. H., Über die Gibbssche Erscheinung etc., M.A. 72 (1912), 228–61.Google Scholar
[2] Gbonwall, T. H., Zur Gibbsschen Erscheinung, Ann. Math. 31 (1930), 232–40.Google Scholar
[3] Gbonwall, T. H., On the Fourier coefficients of a continuous function, B.A.M.S. 27 (1921), 320–1.Google Scholar
[4] Gbonwall, T. H., tiber eine Summationsmethode und ihre Anwendung auf die Fouriersche Reihe, J.f.M. 147 (1916), 16–35.Google Scholar
[1] Grosz, W., Zur Poissonschen Summierung, Wiener Berichte, 124 (1915), 1017–37.Google Scholar
[1] Grunwald, G., tJber Divergenzerscheinungen der Lagrangeschen Interpolationspolynome, A.S. 7 (1935), 207–21.Google Scholar
[2] Grunwald, G., tJber Divergenzerscheinungen der Lagrangeschen Interpolationspolynome der stetigen Funktionen, Ann. Math. 37 (1936), 908–18.Google Scholar
[1] Hardy, G. H., Weierstrass's non-differentiable function, T.A.M.S. 17 (1916), 301–25.Google Scholar
[2] Hardy, G. H., Notes on some points in the integral calculus (LXIV), M.M. 57 (1928), 12–16.Google Scholar
[3] Hardy, G. H., On the summability of Fourier series, P.L.M.S. 12 (1913), 365–72.Google Scholar
[4] Hardy, G. H., Notes on some points in the integral calculus (LVI), M.M. 52 (1922), 49–53.Google Scholar
[5] Hardy, G. H., Notes on some points in the integral calculus (LV), M.M. 51 (1922), 186–92.Google Scholar
[6] Hardy, G. H., A new proof of the functional equation of the Zeta-function, Matematisk Tidskrift, B, 1922, pp. 71–3.
[7] Hardy, G. H., A theorem concerning Taylor's séries, Q.J. 44 (1913), 147–60.Google Scholar
[8] Hardy, G. H., Remarks on three recent notes in the Journal, J.L.M.S. 3 (1928), 166–9.Google Scholar
[9] Hardy, G. H., The mean value of the modulus of an analytic function, P.L.M.S. 14 (1914), 269–77.Google Scholar
[10] Hardy, G. H., The multiplication of conditionally convergent séries, P.L.M.S. 6 (1908), 410–23.Google Scholar
[11] Hardy, G. H., Notes on special systems of orthogonal functions (IV): the orthogonal functions of Whittaker's cardinal séries, Proc. Camb. Phil. Soc. 37 (1941), 331–48.Google Scholar
[12] Hardy, G. H., A problem of Diophantine approximation, J. Indian Math. Soc. 11 (1919), 162–6.Google Scholar
[1] Hardy, G. H. and Littlewood, J. E., A maximal theorem with function-theoretic applications, A.M. 54 (1930), 81–116.Google Scholar
[2] Hardy, G. H. and Littlewood, J. E., Some new convergence criteria for Fourier series, J.L.M.S. 7 (1932), 252–6.Google Scholar
[3] Hardy, G. H. and Littlewood, J. E., Some new convergence criteria for Fourier series, Annali di Pisa, 3 (1934), 43–62.Google Scholar
[4] Hardy, G. H. and Littlewood, J. E., Sur la série de Fourier d'une fonction à carré sommable, C.R. 156 (1913), 1307–9.Google Scholar
[5] Hardy, G. H. and Littlewood, J. E., On the absolute convergence of Fourier series, J.L.M.S. 3 (1928), 250–3.Google Scholar
[6] Hardy, G. H. and Littlewood, J. E., On the strong summability of Fourier séries, F.M. 25 (1935), 162–89.Google Scholar
[7] Hardy, G. H. and Littlewood, J. E., The allied séries of a Fourier séries, P.L.M.S. 24 (1925), 211–46.Google Scholar
[8] Hardy, G. H. and Littlewood, J. E., The Fourier séries of a positive function, J.L.M.S. 1 (1926), 134–8.Google Scholar
[9] Hardy, G. H. and Littlewood, J. E., Some properties of fractional integral (I), M.Z. 28 (1928), 565–606; (II), M.Z. 34 (1931-2), 403-39.Google Scholar
[10] Hardy, G. H. and Littlewood, J. E., A convergence criterion for Fourier séries, M.Z. 28 (1928), 612–34.Google Scholar
[11] Hardy, G. H. and Littlewood, J. E., Some problems of Diophantine approximation: A remarkable trigonometrical séries, Proc. Nat. Acad. U.S.A. 2 (1916), 583–6.Google Scholar
[12] Hardy, G. H. and Littlewood, J. E., Solution of the Cesàro summability problem for power séries and Fourier series, M.Z. 19 (1923), 67–96.Google Scholar
[13] Hardy, G. H. and Littlewood, J. E., Some properties of conjugate functions, J.f.M. 167 (1932), 405–23.Google Scholar
[144 Hardy, G. H. and Littlewood, J. E., Some theorems on Fourier séries and Fourier power séries, Duke J. 2 (1936), 354–81.Google Scholar
[15] Hardy, G. H. and Littlewood, J. E., Some new properties of Fourier constants, M.A. 97 (1926), 159–209.Google Scholar
[16] Hardy, G. H. and Littlewood, J. E., Two theorems concerning Fourier séries, J.L.M.S. 1 (1926), 19–25.Google Scholar
[17] Hardy, G. H. and Littlewood, J. E., A further note on the converse of Abel's theorem, P.L.M.S. 25 (1926), 219–36.Google Scholar
[18] Hardy, G. H. and Littlewood, J. E., Taüberian theorems' concerning power séries and Dirichlet séries whose coefficients are positive, P.L.M.S. 13 (1914), 174–91.Google Scholar
[19] Hardy, G. H. and Littlewood, J. E., Theorems concerning mean values of analytic or harmonic functions, Q.J. 12 (1942), 221–56.Google Scholar
[20] Hardy, G. H. and Littlewood, J. E., Some new cases of Parseval's theorem, M.Z. 34 (1932), 620–33.Google Scholar
[21] Hardy, G. H. and Littlewood, J. E., On the partial sums of Fourier séries, Proc. Camb. Phil. Soc. 40 (1944), 103–7.Google Scholar
[22] Hardy, G. H. and Littlewood, J. E., Some new properties of Fourier constants, J.L.M.S. 6 (1931), 3–9.Google Scholar
[23] Hardy, G. H. and Littlewood, J. E., A problem concerning majorants of Fourier séries, Q.J. 6 (1935), 304–15.Google Scholar
[24] Hardy, G. H. and Littlewood, J. E., Generalizations of a theory of Paley, Q.J. 8 (1937), 161–71.Google Scholar
[25] Hardy, G. H. and Littlewood, J. E., On the Fourier séries conjugate to the Fourier séries of a bounded function, J.L.M.S. 6 (1931), 278–86.Google Scholar
[26] Hardy, G. H. and Littlewood, J. E., On Young's convergence criterion for Fourier séries, P.L.M.S. 28 (1928), 301–11.Google Scholar
[1] Hardy, G. H. and Rogosinski, W. W., On the Gibbs phenomenon, J.L.M.S. 18 (1943), 83–7.Google Scholar
[2] Hardy, G. H. and Rogosinski, W. W., Asymptotic expressions for sums of certain trigonometric séries, Q.J. 16 (1945), 49–58.Google Scholar
[3] Hardy, G. H. and Rogosinski, W. W., On sine séries with positive coefficients, J.L.M.S. 18 (1943), 50–7.Google Scholar
[1] Hartman, Ph., The divergence of non-harmonic gap séries, Duke J. 9 (1942), 404–5.Google Scholar
[1] Haetman, Ph. and Wintner, A., A sine séries with monotonic coefficients, J.L.M.S. 28 (1953), 102–4.Google Scholar
[1] Hausdorff, F., Eine Ausdehnung des Parsevalschen Satzes über Fourier-reihen, M.Z. 16 (1923), 163–9.Google Scholar
[1] Helson, H., Proof of a conjecture of Steinhaus, Proc. Nat. Acad. U.S.A. 40 (1954), 205–6.Google Scholar
[2] Helson, H., Fourier transforms on perfect sets, S.M. 14 (1954), 209–13.Google Scholar
[1] Herglotz, G., tiber Potenzreihen mit positivem reellem Teil im Einheitskreise, Leipziger Berichte, 63 (1911), 501–11.Google Scholar
[1] Herriot, J. G., Nörlund summability of multiple Fourier series, Duke J. 11 (1944), 735–54.Google Scholar
[1] Herzog, F. and Piranian, J., Sets of convergence of Taylor séries (I), Duke J. 16 (1949), 529–34; (II), ibid. 20 (1953), 41–54.Google Scholar
[1] Hewitt, E. and Hirschman, I. I., A maximum problem in harmonic analysis, A.J.M. 76 (1954), 839–51.Google Scholar
[1] Heywo∧D, Ph., A note on a theorem of Hardy on trigonometrical séries, J.L.M.S. 29 (1954), 373–8.Google Scholar
[2] Heywo∧D, Ph., On the integrability of functions, defined by trigonometric séries, Q.J. 5 (1954), 71–6.Google Scholar
[1] Hille, E., On the analytical theory of semi-groups, Proc. Nat. Acad. U.S.A. 28 (1942), 421–4.Google Scholar
[2] Hille, E., Note on a power séries considered by Hardy and Littlewood, J.L.M.S. 4 (1929), 176–82.Google Scholar
[3] Hille, E., On functions of bounded deviation, P.L.M.S. 31 (1930), 165–73.Google Scholar
[1] Hille, E. and Tamarkin, J. D., On the summability of Fourier séries: (I), T.A.M.S. 34 (1932), 757–83; (II), Ann. Math. 34 (1933), 329–44 and 602-5; (III), M.A. 108 (1933), 525–77.Google Scholar
[2] Hille, E. and Tamarkin, J. D., Remarks on a known example of a monotone function, American Math. Monthly\ 36 (1929), 255–64.Google Scholar
[3] Hille, E. and Tamarkin, J. D., On the theory of Fourier transforms, B.A.M.S. 39 (1933), 768–74.Google Scholar
[1] Hirschman, I. I., A convexity theorem for certain groups of transformations, J. d'Analyse Math. 2 (1953), 209–18.Google Scholar
[2] Hirschman, I. I., Fractional integration, A.J.M. 75 (1953), 531–46.Google Scholar
[1] Hobson, E. W., On the integration of trigonometrical séries, J.L.M.S. 2 (1927), 164–6.Google Scholar
[2] Hobson, E. W., On the uniform convergence of Fourier séries, P.L.M.S. 5 (1907), 275–89.Google Scholar
[1] Hylten-Cavallius, C., Geometrical methods applied to trigonometrical séries, Comm. of the Math. Seminar of the U. of Lund, 1950.
[1] Ingham, A. E., On the ‘high-indices’ theorem of Hardy and Littlewood, Q.J. 8 (1937), 1–7.Google Scholar
[2] Ingham, A. E., Note on a certain power séries, Ann. Math. 31 (1930), 241–5.Google Scholar
[3] Ingham, A. E., Some trigonometric inequalities with applications to the theory of séries, M.Z. 41 (1936), 367–79.Google Scholar
[1] Ivasev-Musatov, O. S., The coefficients of trigonometric null séries (in Russian), Izvestia, 21 (1957), 559–78.Google Scholar
[1] Izumi, S., A simple proof of Littlewood's taüberian theorem, Proc. Japanese Acad. 30 (1954), 927–9.Google Scholar
[1] Jackson, D., Über eine trigonometrische Summe, R.P. 32 (1911), 257–62.Google Scholar
[2] Jackson, D., On approximations by trigonometrical sums and polynomials, T.A.M.S. 13 (1912), 491–515.Google Scholar
[3] Jackson, D., A formula for trigonometric interpolation, R.P. 37 (1914), 371–5.Google Scholar
[4] Jackson, D., On the order of magnitude of coefficients in trigonometric interpolation, T.A.M.S. 21 (1920), 321–32.Google Scholar
[5] Jackson, D., Some notes on trigonometric interpolation, Amer. Math. Monthly, 34 (1927), 401–5.CrossRefGoogle Scholar
[1] James, R. D., A generalized integral (II), Canad. J. Math. 2 (1950), 297–306.Google Scholar
[2] James, R. D., Integrals and summable trigonometric séries, B.A.M.S. 61 (1955), 1–15.Google Scholar
[1] Jessen, B., On the approximation of Lebesgue integrals by Riemann sums, Ann. Math. 35 (1934), 248–51.Google Scholar
[1] Jessen, B., Marcinkiewicz, J. and Zygmund, A., Note on the differentiability of multiple integrals, F.M. 25 (1935), 217–34.Google Scholar
[1] Kac, M., Convergence and divergence of non-harmonic gap séries, Duke J. 8 (1941), 541–5.Google Scholar
[2] Kac, M., On a theorem of Zygmund, Proc. Camb. Phil. Soc. 47 (1951), 475–6.Google Scholar
[1] Kaczmarz, S., Über ein Orthogonalsystem, Comptes Rendus du I Congrès des mathématiciens des pays slaves (Warszawa, 1929), pp. 189–92.
[2] Kaczmarz, S., Integrate vom Dinischen typus, S.M. 3 (1931), 189–99.Google Scholar
[3] Kaczmarz, S., The divergence of certain integrals, J.L.M.S. 7 (1932), 218–22.Google Scholar
[4] Kaczmarz, S., On some classes of Fourier séries, J.L.M.S. 8 (1933), 39–46.Google Scholar
[1] Kaczmarz, S. and Marcinkiewicz, J., Sur les multiplicateurs des séries orthogonales, S.M. 7 (1938), 73–81.Google Scholar
[1] Kahane, J. P., Généralisation d'un théorème de S. Bernstein, B.S.M.F. 85 (1957), 221–8.Google Scholar
[1] Kahane, J. P. and Salem, R., Sur les ensembles lineaires non portant pas de pseudomesures, C.R. 243 (1956), 1185–7.Google Scholar
[2] Kahane, J. P. and Salem, R., Construction de pseudomesures sur les ensembles parfaits symétriques, C.R. 243 19861988.Google Scholar
[1] Karamata, J., Über die Hardy-Littlewoodsche Umkehrungen des Abelschen StetigkeitssatzesM.Z. 32 (1930), 319–20.Google Scholar
[2] Karamata, J., Sur un mode de croissance régulière, B.S.M.F. 61 (1933), 55–62.Google Scholar
[3] Karamata, J., Sur la sommabilité de S. Bernstein et quelques procédés qui s'y rattachent, Sbornik, 21 (1947), 13–22.Google Scholar
[4] Karamata, J., Über die Beziehung zwischen dem Bernsteinschen und Cesàroschen Limitierungsverfahren, M.Z. 52 (1949), 305–6.Google Scholar
[5] Karamata, J., Suites des fonctionnelles linéaires et facteurs de convergence des séries de Fourier, Journal de Math. 35 (1956), 87–95.Google Scholar
[6] Karamata, J., Remarque relative à la sommation des séries de Fourier par le procede de Norlund, Publ. Sci. de l'Université d'Alger, Sciences Mathématiques, 1 (1954), 7–14.Google Scholar
[1] Karamata, J. and Tomić, M., Sur la sommation des séries de Fourier des fonctions continues, Publ. Inst. Math. Acad. Serbe, 8 (1955), 123–38.Google Scholar
[1] Khintchin, J., Sur les suites de fonctions analytiques bornees dans leur ensemble, F.M. 4 (1923), 72–5.Google Scholar
[1] Khintchin, J. and Kolmogorov, A. N., Über Konvergenz von Reihen deren Glieder durch den Zufall bestimmt werden, Sbornik, 32 (1925), 668–77.Google Scholar
[1] Klein, G., A note on interpolation, P.A.M.S. 1 (1950), 695–702.Google Scholar
[1] Kober, H., A note on Hilbert transforms, J.L.M.S. 18 (1943), 66–71.Google Scholar
[1] Kogbetliantz, E., Recherches sur l'unicité des séries ultra-sphériques, J.M. 5 (1924), 125–96.Google Scholar
[2] Kogbetliantz, E., Analogies entre les séries trigonométriques et les séries sphériques, A.E.N.S. 40 (1923), 259–323.Google Scholar
[1] Kolmogorov, A. N., Zur Grössenordnung des Restgliedes Fourierscher Reihen differenzierbarer Funktionen, Ann. Math. 36 (1935), 521–6.Google Scholar
[2] Kolmogorov, A. N., Sur les fonctions harmoniques conjuguées et les séries de Fourier, F.M. 7 (1925), 23–8.Google Scholar
[3] Kolmogorov, A. N., Sur l'ordre de grandeur des coefficients de la série de Fourier-Lebesgue, B.A.P. (1923), 83–6.Google Scholar
[4] Kolmogorov, A. N., Sur la possibilité de la définition générale de la dérivée, de l'intégrale et de la sommation des séries divergentes, C.R. 180 (1925), 362–4.Google Scholar
[5] Kolmogorov, A. N., Une contribution à l'étude de la convergence des séries de Fourier, F.M. 5 (1924), 96–7.Google Scholar
[6] Kolmogorov, A. N., Une série de Fourier-Lebesgue divergente presque partout, F.M. 4 (1923), 324–8.Google Scholar
[7] Kolmogorov, A. N., Une série de Fourier-Lebesgue divergente partout, C.R. 183 (1926), 1327–8.Google Scholar
[1] Kolmogorov, A. N. and Seliverstov, G., Sur la convergence des séries de Fourier, C.R. 178 (1925), 303–5.Google Scholar
[2] Kolmogorov, A. N. and Seliverstov, G., Sur la convergence des séries de Fourier, Acc. Lincei, 3 (1926), 307–10.Google Scholar
[1] Korn, A., Über Minimal-flächen deren Randcurven wenig von ebenen Kurven abweichen, Abh. K. Preussischen Akadehiie der Wiss., Phys.-Math. Klasse (1909), pp. 1-37.Google Scholar
[1] Krylov, V., Functions regular in a half-plane (in Russian), Sbornik, 6 (1939), 95–138.Google Scholar
[1] Kuttner, B., Some relations between different kinds of Riemann summability, P.L.M.S. 40 (1936), 524–40.Google Scholar
[2] Kuttner, B., A theorem on trigonometric séries, J.L.M.S. 10 (1935), 131–40.Google Scholar
[1] Landau, E., Über eine trigonometrische Ungleichung, M.Z. 37 (1933), 36.Google Scholar
[2] Landau, E., Abschätzungen der Koefnzientensumme einer Potenzreihe, Archiv. Math. Physik, 21 (1913), 42–50.Google Scholar
[1] Lebesgue, H., Sur la représentation trigonométrique approchée des fonctions satisfaisant a une condition de Lipschitz, B.S.M.F. 38 (1910), 184–210.Google Scholar
[2] Lebesgue, H., Recherches sur la convergence des séries de Fourier, M.A. 61 (1905), 251–80.Google Scholar
[1] Lévy, P., L'espace de répartitions linéaires, B.S.M. 62 (1938), 305–20, 324–37.Google Scholar
[2] Levy, P., Sur la convergence absolue des séries de Fourier, Compositio Math. 1 (1934), 1–14.Google Scholar
[1] Littlewood, J. E., On bounded bilinear forms in an infinite number of variables, Q.J. 1 (1930), 164–74.Google Scholar
[2] Littlewood, J. E., On a theorem of Fatou, J.L.M.S. 2 (1927), 172–6.Google Scholar
[3] Littlewood, J. E., The converse of Abel's theorem on power séries, P.L.M.S. 9 (1910), 434–48.Google Scholar
[4] Littlewood, J. E., On Fourier coefficients of functions of bounded variation, Q.J. 7 (1936), 219–26.Google Scholar
[5] Littlewood, J. E., On a theorem of Paley, J.L.M.S. 29 (1954), 387–95.Google Scholar
[6] Littlewood, J. E., On mean values of power séries, P.L.M.S. 25 (1924), 328–37.Google Scholar
[7] Littlewood, J. E., On mean values of power séries, J.L.M.S. 5 (1930), 179–82.Google Scholar
[1] Littlewood, J. E. and PALEY, R. E. A. C., Theorems on Fourier séries and power séries, (I)J.L.M.S. 6 (1931), 230–3; (II) P.L.M.S. 42 (1936), 52–89; (III) ibid. 43 (1937), 105–26.Google Scholar
[1] Loomis, L., A note on Hilbert's transform, B.A.M.S. 52 (1946), 1082–6.Google Scholar
[1] Lozinski, S., On convergence and summability of Fourier séries and interpolation processes, Sbornik, 14 (1944), 175–263.Google Scholar
[1] Ltjkacs, F., Über die Bestimmung des Sprunges einer Funktion aus ihrer Fourierreihe, J.f.M. 150 (1920), 107–12.Google Scholar
[1] Lusin, N., Integral and trigonometric séries (in Russian) (Moscow, 1915); second edition (Moscow, 1951) (with critical and historical annotations by N. Bary and D. E. Mensov); also reprinted in Lusin's Collected Works. [2] Sur l'absolue convergence des séries trigonométriques, C.R. 155 (1912), 580–2.
[3] Lusin, N., Über eine Potenzreihe, R.P. 32 (1911), 386–90.Google Scholar
[4] Lusin, N., On the localization of the principle of finite area, Doklady, 56 (1947), 447–50.Google Scholar
[5] Lusin, N., Sur une propriété des fonctions à carré sommable, Bull. Calcutta Math. Soc. 20 (1930), 139–54.Google Scholar
[1] Lusin, N. and Privalov, I., Sur l'unicité et la multiplicité des fonctions analytiques, A.E.N.S. 42 (1925), 143–91.Google Scholar
[1] Luxemburg, W. A. J., Banach function spaces, Diss. (Delft, 1955), pp. 1-70.
[1] Malliavin, P., Sur la convergence absolue des séries trigonométriques, C.R. 228 (1949), 1467–9.Google Scholar
[1] Mandelbrojt, S., Modern researches on the singularities of functions defined by Taylor's séries, Rice Institute Pamphlets, 14 (1927), no. 4, 225–32.Google Scholar
[2] Mandelbrojt, S., Some theorems connected with the theory of infinitely differentiate functions, Duke J. 11 (1944), 341–9.Google Scholar
[1] Mabcinkiewicz, J., Sur quelques intégrales du type de Dini, Ann. de la Soc. Polonaise de Math. 17 (1938), 42–50.Google Scholar
[2] Mabcinkiewicz, J., Sur les séries de Fourier, F.M. 27 (1936), 38–69.Google Scholar
[3] Mabcinkiewicz, J., Quelques théorèmes sur les séries de fonctions, Bull, du Seminaire Math, de l'Université de Wilno, 1 (1937).Google Scholar
[4] Marcinkiewicz, J., On Riemann's two methods of summation, J.L.M.S. 10 (1935), 268–72Google Scholar
[5] Marcinkiewicz, J., On the convergence of Fourier séries, J.L.M.S. 10 (1935) pp. 264–8.Google Scholar
[6] Marcinkiewicz, J., A new proof of a theorem on Fourier séries, J.L.M.S. 8 (1933), 179.Google Scholar
[7] Marcinkiewicz, J., On interpolating polynomials (in Polish), Wiadomości Matematyczne, 39 (1935), 85–125.Google Scholar
[8] Marcinkiewicz, J., Sur la divergence des polynomes d'interpolation, A.S. 8 (1937), 131–5.Google Scholar
[9] Marcinkiewicz, J., Quelques remarques sur Vinterpolation, A.S. 8 (1937), pp. 127–30.Google Scholar
[10] Marcinkiewicz, J., Sur Interpolation, S.M. 6 (1936), 1–17, 67-81.Google Scholar
[11] Marcinkiewicz, J., Sur la sommabilité forte des séries de Fourier, J.L.M.S. 14 (1939), 162–8.Google Scholar
[12] Marcinkiewicz, J., Sur les multiplicateurs des séries de Fourier, S.M. 8 (1939), 78–91.Google Scholar
[13] Marcinkiewicz, J., Sur une nouvelle condition sur la convergence presque partout des séries de Fourier, Ann. Pisa, 8 (1939), 139–40.Google Scholar
[14] Marcinkiewicz, J., Sur Interpolation d'opérations, C.R. 208 (1939), 1272–3.Google Scholar
[1] Marcinkiewicz, J. and Zygmund, A., Quelques théorèmes sur les fonctions indépendantes, S.M. 7 (1938), 104–20.Google Scholar
[2] Marcinkiewicz, J. and Zygmund, A., On the differentiability of functions and summability of trigonometrical séries, F.M. 26 (1936), 1–43.Google Scholar
[3] Marcinkiewicz, J. and Zygmund, A., Two theorems on trigonometrical séries, Sbornik, 2 (1937), 733–8.Google Scholar
[4] Marcinkiewicz, J. and Zygmund, A., Some theorems on orthogonal systems, F.M. 28 (1937), 309–35.Google Scholar
[5] Marcinkiewicz, J. and Zygmund, A., Quelques inégalités pour les opérations linéaires, F.M. 32 (1939), 115–21.Google Scholar
[6] Marcinkiewicz, J. and Zygmund, A., Mean values of trigonometric polynomials, F.M. 28 (1937), 131–66.Google Scholar
[7] Marcinkiewicz, J. and Zygmund, A., On the behavior of trigonometric séries and power séries, T.A.M.S. 50 (1941), 407–63.Google Scholar
[8] Marcinkiewicz, J. and Zygmund, A., A theorem of Lusin, Duke J. 4 (1938), 473–85.Google Scholar
[9] Marcinkiewicz, J. and Zygmund, A., On the summability of double Fourier séries, F.M. 32 (1939), 112–32.Google Scholar
[1] Mazurkiewicz, S., Sur l'intégrale. S.M. 3 (1931), 114–18.Google Scholar
[2] Mazurkiewicz, S., Sur les séries de puissances et les séries trigonométriques non sommables (in Polish, with a French summary), Prace Matematyczno-Fizyczne, 28 (1919), 109–18.Google Scholar
[3] Mazurkiewicz, S., Sur les séries de puissances, F.M. 3 (1922), 52–8.Google Scholar
[1] MENšOV, D., Sur la convergence uniforme des séries de Fourier (in Russian), Sbornik, 11 (1942), 67–96.Google Scholar
[2] MENšOV, D., Sur l'unicité du développement trigonométrique, C.R. 163 (1916), 433–6.Google Scholar
[3] MENšOV, D., On limits of indeterminacy of Fourier séries (in Russian), Sbornik, 30 (1950), 601–50.Google Scholar
[4] MENšOV, D., On limits of indeterminacy in measure of partial sums of trigonometric séries (in Russian), Sbornik, 34 (1954), 557–74.Google Scholar
[5] MENšOV, D., On the convergence of trigonometric séries (in Russian), A.S. 12 (1950), 170–84.Google Scholar
[6] MENšOV, D., Sur les séries de fonctions orthogonales, (I), F.M. 4 (1923), 82–105; (II), F.M. 8 (1926), 56–108; (III), F.M. 10 (1927), 375–420.Google Scholar
Milicer-Gruzewska, H., Sur les fonctions à variation bornée et à l'écart Hadamardien nul, C.R. Soc. Sci. Varsovie, 21 (1928), 67–78.Google Scholar
[1] Mirimanoff, D., Remarque sur la notion d'ensemble parfait de l-re espèce, F.M. 4(1923), 122–3.Google Scholar
[1] Moore, C. N., On the application of Borel's method to the summation of Fourier séries, Proc. Nat. Acad. U.S.A. 11 (1925), 284–7.Google Scholar
[2] Moore, C. N., On the summability of double Fourier séries of discontinuous functions, M.A. 74 (1913), 555–78.Google Scholar
[1] Morgenthaler, G. W., On Walsh-Fourier séries, T.A.M.S. 84 (1957), 472–507.Google Scholar
[1] Morse, M. and Transue, W., Functionals F bilinear over the product A × B of two pseudonormed vector spaces; I I. Admissible spaces A, Ann. Math. 51 (1950), 576–614.Google Scholar
[1] Mulholland, H. P., Concerning the generalization of the Young-Hausdorff theorem, P.L.M.S. 35 (1933), 257–93.Google Scholar
Natanson, I. P. [1] On the convergence of trigonometrical interpolation at equidistant knots, Ann. Math. 45 (1944), 457–71.Google Scholar
[1] Neder, A., Zur theorie der trigonometrischen Reihen, M.A. 84 (1921), 117–36.Google Scholar
[1] Nevanlinna, R., Über die Anwendung des Poissonschen Integrals zur Untersuchung der Singularitaten analytischer Funktionen, Verh. des 5. Math. Congress, Helsingfors (1923), pp. 273–89.Google Scholar
[1] Niemytski, V., Sur quelques classes d'ensembles lineaires avec applications aux séries trigonométriques absolument convergentes (in Russian, with a French summary), Sbornik, 33 (1926), 5–32.Google Scholar
[1] Nikolsky, S. M., Inequalities for entire functions of finite type and their applications in the theory of differentiate functions of several variables (in Russian), Trudy Mat. Inst. Steklov, 38 (1951), 244–78.Google Scholar
[2] Nikolsky, S. M., Sur Failure asymptotique du reste dans l'approximation au moyen des sommes de Fejér des fonctions vérifiant la condition de Lipschitz (in Russian, with a French summary), Doklady, 4 (1940), 501–8.Google Scholar
[1] Obrechkoff, N., Sur la sommation des séries trigonométriques de Fourier par les moyennes arithmétiques, B.S.M.F. 62 (1934), 84–109, 167–84.Google Scholar
[1] Offord, A.C., Approximation of functions by trigonometric polynomials, Duke J. 6 (1940), 505–10.Google Scholar
[2] Offord, A.C., On the uniqueness of the representation of a function by a trigonometric integral, P.L.M.S. 42 (1937), 422–80.Google Scholar
[1] Orlicz, W., Über eine gewisse Klasse von Raumen von Typus B, B.A.P. 1932, pp. 207–20.Google Scholar
[2] Orlicz, W., Über Raume LM, B.A.P. (1936), pp. 93–107.Google Scholar
[1] Ostrow, E. H. and Stein, E. M., A generalization of lemmas of Marcinkiewicz and Fine with applications to singular integrals, Annali di Pisa, 11 (1957), 117–35.Google Scholar
[1] Ostrowski, A., Über die Bedeutung der Jensenschen Formel fur einige Fragen der Komplexen Funktionentheorie, A.S. 1 (19221923), 80–7.Google Scholar
[1] Paley, R. E. A. C., A remarkable system of orthogonal functions, P.L.M.S. 34 (1932), 241–79.Google Scholar
[2] Paley, R. E. A. C., On lacunary power séries, Proc. Nat. Acad. U.S.A. 19 (1933), 271–2.Google Scholar
[3] Paley, R. E. A. C., Some theorems on orthogonal functions, S.M. 3 (1931), 226–45.Google Scholar
[4] Paley, R. E. A. C., A proof of a theorem on bilinear forms, J.L.M.S. 6 (1931), 226–30.Google Scholar
[5] Paley, R. E. A. C., On the lacunary coefficients of power séries, Ann. Math. 34 (1933), 615–16.Google Scholar
[6] Paley, R. E. A. C., A note on power séries, J.L.M.S. 7 (1932), 122–30.Google Scholar
[7] Paley, R. E. A. C., On Fourier séries with positive coefficients, P.L.M.S. 7 (1932), 205–8.Google Scholar
[1] Paley, R. E. A. C. and Zygmund, A., On some séries of functions, (I)Proc. Camb. Phil. Soc. 26 (1930), 337–57; (II), Proc. Camb. Phil. Soc. 458-74; (III), Proc. Camb. Phil. Soc. 28 (1932), 190–205.CrossRefGoogle Scholar
[2] Paley, R. E. A. C. and Zygmund, A., On the partial sums of Fourier séries, S.M. 2 (1930), 221–7.Google Scholar
[3] Paley, R. E. A. C. and Zygmund, A., A note on analytic functions inside the unit circle, Proc. Camb. Phil. Soc. 28 (1932), 266–72.Google Scholar
[1] Papotjlis, A., On the strong differentiability of the indefinite integral, T.A.M.S. 69 (1950), 130–41.Google Scholar
[1] Phragmén, E., Några reflexioner i anknytning till Dr Riesz's föredrag, 3rd Scandinavian Math. Congress, Kristiania (1913), pp. 129–42.Google Scholar
[1] Piranian, G. and Rudin, W., Lusin's theorem on areas of conformal maps, Michigan Math. J. 3 (19551956), 191–9.Google Scholar
[1] Pisot, Ch., Sur la répartition modulo 1, Annali di Pisa, 7 (1938), 205–48.Google Scholar
[2] Pisot, Ch., Sur une famille remarquable d'entiers algébriques formant un ensemble fermé, Colloque sur la théorie des nombres, Bruxelles (1955), pp. 77-83.
[1] Pitt, H. R., Theorems on Fourier séries and power séries, Duke J. 3 (1937), 747–55.Google Scholar
[1] Plancherel, M., Le développement de la théorie des séries trigonométriques dans le dernier quart de siècle, Enseignement Mathématique, 24 (1925).Google Scholar
[2] Plancherel, M., Contribution à l'étude de la représentation d'une fonction arbitraire par des intégrates definies, R.P. 30 (1910), 289–335.Google Scholar
[3] Plancherel, M., Sur la convergence et la sommabilité par les moyennes de Cesàro de limM.A. 76 (1915), 315–26.Google Scholar
[1] Plessner, A., Eine Kennzeichnung der totalstetigen Funktionen, J.f.M. 160 (1929), 26–32.Google Scholar
[2] Plessner, A., Zur Theorie der konjugierten trigonometrischen Reihen, Mitt. Math. Seminar Universitdt Giessen, 10 (1923), 1–36.Google Scholar
[3] Plessner, A., Über die Konvergenz von trigonometrischen Reihen, J.f.M. 155 (1926), 15–25.Google Scholar
[4] Plessner, A., Über konjugierte trigonometrische Reihen, Doklady, 4 (1935), 251–3.Google Scholar
[5] Plessner, A., tiber die Verhalten analytischer Funktionen am Rande ihres Definitionsbereiches, J.f.M. 159 (1927), 219–27.Google Scholar
[1] Pollard, H., The harmonic analysis of bounded functions, Duke J. 20 (1953), 499–512.Google Scholar
[1] Prasad, B. N., On the summability of Fourier séries and the bounded variation of power séries, P.L.M.S. 35 (1933), 407–24.Google Scholar
[2] Prasad, B. N., A theorem on the summability of the allied séries of a Fourier séries, J.L.M.S. 6 (1931), 274–8.Google Scholar
[1] Privalov, I. I., Intégrate de Cauchy (in Russian), Saratov (1919), pp. 1-104.Google Scholar
[2] Privalov, I. I., Sur les fonctions conjuguées, B.S.M.F. 44 (1916), 100–3.Google Scholar
[1] Pyatetski-Shapiro, I. I., On the problem of uniqueness of expansion of a function in a trigonometric séries (in Russian), Učenye Zapiski Moskovskogo Gosudarstvennogo Universiteta, 155, Matematika, 5 (1952), 54–72.Google Scholar
[2] Pyatetski-Shapiro, I. I., Supplement to the work ‘On the problem, etc.’, Učenye Zapiski Moskovskogo Gosudarstvennogo Universiteta, 155, Matematika 165, 7 (1954), 78–97.Google Scholar
[1] Quade, E. S., Trigonometric approximation in the mean, Duke J. 3 (1937), 529–43.Google Scholar
[1] Rademacher, H., Einige Sätze über Reihen von allgemeinen Orthogonalfunktionen, M.A. 87 (1922), 112–38.Google Scholar
[1] Rajchman, A., SÉRies trigonométriques sommables par le procede de Poisson (in Polish, French summary), Prace Matematyczno-Fizyczne, 30 (1919), 19–88.Google Scholar
[2] Rajchman, A., Sur l'unicité de développement trigonométrique, F.M. 3 (1922), 286–302.Google Scholar
[3] Rajchman, A., Sur le principe de localisation de Riemann (in Polish, French summary), Comptes Rendus de la Soc. Sci. de Varsovie, 11 (1918), 115–22.Google Scholar
[4] Rajchman, A., Sur la multiplication des séries trigonométriques et sur une classe d'ensembles fermes. M.A. 95 (1926), 388–408.Google Scholar
[5] Rajchman, A., Sur la convergence multiple, C.R. 181 (1925), 172–4.Google Scholar
[6] Rajchman, A., Une classe de séries trigonométriques qui convergent presque partout vers zero, M.A. 101 (1929), 686–700.Google Scholar
[7] Rajchman, A., Sur une classe de fonctions à variation bornée, C.R. 187 (1928), 1026–8.Google Scholar
[1] Rajchman, A. and Zygmund, A., Sur la possibilité d'appliquer la méthode de Riemann aux séries trigonométriques sommables par le procédé de Poisson, M.Z. 25 (1926), 261–73.Google Scholar
[2] Rajchman, A. and Zygmund, A., Sur la relation du procédé de sommation de Cesàro et celui de Riemann, B.A.P. (1925), pp. 69-80.Google Scholar
[1] Randels, W. C., On an approximate functional equation of Paley, T.A.M.S. 43 (1938), 102–25.Google Scholar
[1] Reiter, H., On a certain class of ideals in the L1-algebra of a locally compact abelian group, T.A.M.S. 75 (1953), 505–9.Google Scholar
[1] Riemann, B., Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe, Ges. Werke, 2 Aim., Leipzig (1892), pp. 227–71.Google Scholar
[1] Riesz, F., Sur les polynômes trigonométriques, C.R. 158 (1914), 1657–61.Google Scholar
[2] Riesz, F., Über orthogonale Funktionensysteme, Göttinger Nachrichten (1907), pp. 116–22.Google Scholar
[3] Riesz, F., Sur certains systemes singuliers d'équations intégrates, A.E.N.S. 28 (1911), 33–62.Google Scholar
[4] Riesz, F., Eine Ungleichung für harmonische Funktionen, M.f.M. 43 (1936), 401–6.Google Scholar
[5] Riesz, F., Über ein Problem von Caratheodory, J.f.M. 146 (1916), 83–7.Google Scholar
[6] Riesz, F., Über die Fourierkoemzienten einer stetigen Funktion von beschrankter Schwankung, M.Z. 2 (1918), 312–15.Google Scholar
[7] Riesz, F., Über die Randwerte einer analytischen Funktion, M.Z. 18 (1923), 87–95.Google Scholar
[8] Riesz, F., Über eine Verallgemeinerung des Parsevalschen Formel, M.Z. 18 (1923), 117–24.Google Scholar
[1] Riesz, F. and M., Über Randwerte einer analytischen Funktion, Quatrieme Congres des mathematiciens scandi?iaves, Stockholm (1916), pp. 27-44.
[1] Riesz, M., Sur les fonctions conjuguees, M.Z. 27 (1927), 218–44.Google Scholar
[2] Riesz, M., Sur la sommation des séries de Fourier, A.S., 1 (1923), 104–13.Google Scholar
[3] Riesz, M., Eine trigonometrische Interpolationsformel und einige Ungleichungen fur Polynome, Jahresbericht d. Deutschen Math. Ver. 23 (1914), 354–68.Google Scholar
[4] Riesz, M., Sur les maxima des formes bilineaires et sur les fonctionnelles lineaires, A.M. 49 (1926), 465–97.Google Scholar
[5] Riesz, M., Neuer Beweis des Fatouschen Satzes, Gottinger Nachrichten (1916), pp. 62–5.
[6] Riesz, M., Satze tiber Potenzreihen, Arkiv for Matematik, Astronomi och Fysik, 11 (1916), no. 12.Google Scholar
[7] Riesz, M., Summierbare trigonometrische Reihen, M.A. 71 (1911), 54–75.Google Scholar
[1] Rogosinski, W., Über positive harmonische Entwickelungen und typisch reelle Potenzreihen, M.Z. 35 (1932), 93–121.Google Scholar
[2] Rogosinski, W., tiber die Abschnitte trigonometrischer Reihen, M.A. 95 (1925), 110–34.Google Scholar
[3] Rogosinski, W., Reihensummierung durch Abschnittskoppelungen, M.Z. 25 (1926), 132–49.Google Scholar
[4] Rogosinski, W., Abschnittsverhaltungen bei trigonometrischen und insbesondere Fourierschen Reihen, M.Z. 41 (1936), 75–136.Google Scholar
[1] Rogosinski, W. and Szego, G., Über die Abschnitte von Potenzreihen die in einem Kreise beschrankt bleiben, M.Z. 28 (1928), 73–94.Google Scholar
[1] Rudin, W., Radial cluster sets of analytic functions, B.A.M.S. 60 (1954), 545, Abstract no. 718.Google Scholar
[1] Saks, S., On some functionals, (I)T.A.M.S. 35 (1933), 549–56; (II) ibid. 41 (1937), 160–70.Google Scholar
[2] Saks, S., On the strong derivatives of functions of intervals, F.M. 25 (1935), 245–52.Google Scholar
[1] Salem, R., On the absolute convergence of trigonometric séries, Duke J. 8 (1941), 317–34.Google Scholar
[2] Salem, R., Essais sur les séries trigonométriques, Actualités scientifiques et industrielles, no. 862 (Paris, 1940), pp. 1-85.
[3] Salem, R., On a theorem of Bohr and Pàl, B.A.M.S. 50 (1944), 579–80.Google Scholar
[4] Salem, R., Sur les transformations des séries de Fourier, F.M. 33 (1939), 108–14.Google Scholar
[5] Salem, R., A singularity of the Fourier séries of a continuous function, Duke J. 10 (1943), 711–16.Google Scholar
[6] Salem, R., On some properties of symmetrical perfect sets, B.A.M.S. 47 (1941), 820–8.Google Scholar
[7] Salem, R., On a theorem of Zygmund, Duke J. 10 (1943), 23–31.Google Scholar
[8] Salem, R., On sets of multiplicity for trigonometric séries, A.J.M. 64 (1942), 69–82.Google Scholar
[9] Salem, R., On singular monotonic functions of Cantor type, J. Math. Plajsics, 21 (1942), 69–82.Google Scholar
[10] Salem, R., On a problem of Smithies, Indagationes Math. 16 (1954), 403–7.Google Scholar
[11] Salem, R., On singular monotonic functions whose spectrum has a given dimension, Arkiv for Mat. 1 (1951), 353–65.Google Scholar
[12] Salem, R., (I) Sets of uniqueness and sets of multiplicity, T.A.M.S. 54 (1943), 218–28; (II) ibid. 56 (1944), 32–49; (III) Rectification to the papers: Sets of uniqueness and sets of multiplicity, I and II, ibid. 63 (1948), 595–8.Google Scholar
[13] Salem, R., A remarkable class of algebraic integers, Duke J. 11 (1944), 103–8.Google Scholar
[14] Salem, R., New theorems on the convergence of Fourier séries, Koninklijke Nederlandse Akad. Wettenschappen, Math. Sci. (1954), pp. 550–7.
[15] Salem, R., Convexity theorems, B.A.M.S. 55 (1949), 851–60.Google Scholar
[16] Salem, R., Sur une extension du théorème de convexité de M. Marcel Riesz, Colloquium Math. 1 (1947), 6–8.Google Scholar
[17] Salem, R., A new proof of a theorem of Menchoff, Duke J. 8 (1941), 269–72.Google Scholar
[1] Salem, R. and Zygmund, A., On a theorem of Banach, Proc. JVaJ. A cad. U.S.A. 33 (1947), 293–5.
[2] Salem, R. and Zygmund, A., Trigonometric séries whose terms have random sign, A.M. 91 (1954), 245–301.Google Scholar
[3] Salem, R. and Zygmund, A., The approximation by partial sums of Fourier séries, T.A.M.S. 59 (1946), 14–22.Google Scholar
[4] Salem, R. and Zygmund, A., Lacunary power séries and Peano curves, Duke J. 12 (1945), 569–78.Google Scholar
[5] Salem, R. and Zygmund, A., La loi du logarithme itéré pour les séries trigonométriques lacunaires, B.S.M. 74 (1950), 209–24.Google Scholar
[6] Salem, R. and Zygmund, A., A convexity theorem, Proc. Nat. Acad. U.S.A. 34 (1948), 443–7.Google Scholar
[7] Salem, R. and Zygmund, A., On lacunary trigonometric séries, (1)Proc. Nat. Acad. U.S.A. 33 (1947), 333–8; (II), ibid. 34 (1948), 54–62.Google Scholar
[8] Salem, R. and Zygmund, A., Sur un théorème de Piatetski-Shapiro, C.R. 240 (1955), 2040–2.Google Scholar
[9] Salem, R. and Zygmund, A., Sur les enseméles parfaits dissymétriques à rapport constant, C.R. 240 2281–3.
[10] Salem, R. and Zygmund, A., Capacity of sets and Fourier séries, T.A.M.S. 59 (1946), 23–41.Google Scholar
[1] Schaeffer, A. C., The Fourier-Stieltjes coefficients of a function of bounded variation, A.J.M. 61 (1939), 934–40.Google Scholar
[2] Schaeffer, A. C., Inequalities of A. Markoff and S. Bernstein for polynomials and related functions, B.A.M.S. 47 (1941), 565–77.Google Scholar
[3] Schaeffer, A. C., Entire functions and trigonometric polynomials, Duke J. 20 (1953), 77–88.Google Scholar
[1] Schmetterer, L., Zur Fourierentwickelung des Produktes zweier Funktionen, M.f.M. 53 (1949), 53–62.Google Scholar
[2] Schaeffer, A. C., Bemerkungen zur Multiplikation unendlicher Reihen, M.Z. 54 (1951), 102–14.Google Scholar
[1] Schoenberg, I., Über die asymptotische Verteilung reeller Zahlen mod 1, M.Z. 28 (1928), 171–99.Google Scholar
[1] Schur, I., Über lineare Transformationen in der Theorie der unendlichen Reihen, J.f.M. 151 (1921), 79–111.Google Scholar
[1] Schur, I. and Szegö, G., Über die Abschnitte einer im Einheitskreise beschränkter Potenzreihen, Sitzungsberichte d. Berliner Akad. (1925), pp. 545–60.Google Scholar
[1] Seidel, V., On the distribution of values of bounded analytic functions, T.A.M.S. 36 (1934), 200–26.Google Scholar
[1] Sidon, S., Über die Fourierkoeffizienten einer stetigen Funktion von beschränkter Schwankung, A.S. 2 (1924), 43–6.Google Scholar
[2] Sidon, S., Reihentheoretische Sätze und ihre Anwendungen in der Theorie der Fourierschen Reihen, M.Z. 10 (1921), 121–7.Google Scholar
[3] Sidon, S., Verallgemeinerung eines Satzes über die absolute Konvergenz von Fourierreihen mit Lücken, M.A. 97 (1927), 675–6.Google Scholar
[4] Sidon, S., Einige Sätze und Fragestellungen über Fourierkoeffizienten, M.Z. 34 (1932), 477–80.Google Scholar
[5] Sidon, S., Ein Satz über trigonometrische Polynome und ihre Anwendungen in der Theorie der Fourierreihen, M.A. 106 (1932), 536–9.Google Scholar
[1] Sierpiński, W., Sur l'ensemble des points de convergence d'une suite de fonctions continues. F.M. 2 (1921), 41–9.Google Scholar
[1] Smirnov, V., Sur les valeurs limites des fonctions analytiques, C.R. 188 (1929), 131–3.Google Scholar
[2] Smirnov, V., Sur les valeurs limites des fonctions régulières a l'intérieur d'un cercle, Journal de la Soc. Physico-Mathématique de Leningrad, 2 (1929), 22–37.Google Scholar
[1] Šneider, A. A., On the uniqueness of expansions in Walsh functions (in Russian), Sbornik, 24 (1949), 279–300.Google Scholar
[2] Šneider, A. A., On the convergence of subsequences of the partial sums of Fourier séries of Walsh functions, Doklady, 70 (1950), 969–71.Google Scholar
[1] Spencer, D., A function theoretic identity, A.J.M. 65 (1943), 147–60.Google Scholar
[1] Stečkin, S. B., On the absolute convergence of Fourier séries (in Russian), Izvestia, 17 (1953), 499–512; (II) ibid. 19 (1955), 221–46; (III) ibid. 20 (1956), 385–412.Google Scholar
[1] Stein, E., Functions of exponential type, Ann. of Math. 65 (1957), 582–92.Google Scholar
[2] Stein, E., Interpolation of linear operators, T.A.M.S. 83 (1956), 482–92.Google Scholar
[3] Stein, E., A maximal function with applications to Fourier séries, Ann. Math. (1958).
[1] Stein, E. and Weiss, G., Interpolation of operators with change of measures, T.A.M.S. 87 (1958), 159–72.Google Scholar
[2] Stein, E. and Weiss, G., On the interpolation of analytic families of operators acting on Hp-spaces, Tôhoku Mathematical Journal, 9 (1957), 318–39.CrossRefGoogle Scholar
[3] Stein, E. and Weiss, G., An extension of a theorem of Marcinkiewicz and some of its applications, Journal of Math, and Mechanics, 8 (1959).Google Scholar
[1] Stein, P., On a theorem of M. Riesz, J.L.M.S. 8 (1933), 242–7.Google Scholar
[1] Steinhaus, H., Sur le développement du produit de deux fonctions en une série de Fourier, Bull, de l'Ac. de Cracovie (1913), pp. 113–16.
[2] Steinhaus, H., Sur quelques proprétiés de séries trigonométriques et celles de puissances (in Polish, with a French summary), Rozprawy Akademji Umiejetnoici (Cracow, 1915), pp. 175-225.
[3] Steinhaus, H., Über die Wahrscheinlickheit dafür, dass der Konvergenzkreis einer Potenzreihe ihre naturliche Grenze ist, M.Z. 21 (1929), 408–16.Google Scholar
[4] Steinhaus, H., A new property of G. Cantor's set (in Polish), Wektor, 7 (1917).Google Scholar
[5] Steinhaus, H., Sur les distances des points des ensembles de mesure positive, F.M. 1 (1920), 93–104.Google Scholar
[6] Steinhaus, H., Sur la convergence non-uniforme des séries de Fourier, Bull, de l'Ac. de Cracovie (1913), pp. 145–60.
[7] Steinhaus, H., A generalization of G. Cantor's theorem on trigonometric séries (in Polish), Wiadomotci Matematyczne, 24 (1920), 197–201.Google Scholar
[8] Steinhaus, H., Une série trigonométrique partout divergente, Comptes Rendus de la Soc. Sci. Varsovie (1912), pp. 219–29.
[9] Steinhaus, H., A divergent trigonometrical séries, J.L.M.S. 4 (1929), 86–8.Google Scholar
[10] Steinhaus, H., Sur un problèmede MM. Lusin et Sierpiński, Bull. del'Acad. de Cracovie, 1913, 335-350.
[1] Sunouchi, G., On the summability of power séries and Fourier séries, Tôhoku Math. Journal, 7 (1955), 96–109.CrossRefGoogle Scholar
[2] Sunouchi, G., Theorems on power séries of the class Hp, Tdhoku Math. Journal, 8 (1956), 125–46.CrossRefGoogle Scholar
[1] Sutton, O. G., On a theorem of Carleman, P.L.M.S. 23 (1925), XLVIII–LI.Google Scholar
[1] Szasz, O., Über den Konvergenzexponent der Fourierschen Reihen, Munchener Sitzungsberichte (1922), pp. 135–50.
[2] Szasz, O., Über die Fourierschen Reihen gewisser Funktionenklassen, M.A. 100 (1928), 530–6.Google Scholar
[1] Szego, G., liber die Lebesgueschen Konstanten bei den Fourierreihen, M.Z. 9 (1921), 163–6.Google Scholar
[2] Szego, G., Über die Randwerte einer analytischen Funktion, M.A. 84 (1921), 232–44.Google Scholar
[3] Szego, G., Über einen Satz des Herrn S. Bernstein, Schriften d. Koenigsberger gelehrten Oes. 5 (1928), 59–70.Google Scholar
[1] Szego, G. and Zygmund, A., On certain mean values of polynomials, Journal d'Analyse Math. 3 (1953/1954), 225–44.Google Scholar
[1] Sz. Nagy, B., Sur une classe generale de procedes de sommation pour les séries de Fourier, Hungarica Acta Math. 13 (1948), 14–52.Google Scholar
[2] Sz. Nagy, B., Approximation von Funktionen durch die arithmetische Mittel ihrer Fourierschen Reihen, A.S. 11 (1946), 71–84.Google Scholar
[3] Sz. Nagy, B., SéRies et intégrates de Fourier des fonctions monotones non-bornées, A.S. 13 (1948), 118–35.Google Scholar
[1] Tamarkin, J. D., Remarks on the theory of conjugate functions, P.L.M.S. 34 (1932), 379–91.Google Scholar
[1] Tamarkin, J. D. and Zygmund, A., Proof of a theorem of Thorin, B.A.M.S. 50 (1944), 279–82.Google Scholar
[1] Taylor, S. J., An integral of Perron's type, Q.J. 6 (1955), 255–74.Google Scholar
[1] Thorin, G. O., An extension of a convexity theorem due to M. Riesz, Kungl. Fysiografiska Saellskapet i Lund Forhaendlinger, 8 (1939), no. 14.Google Scholar
[2] Thorin, G. O., Convexity theorems, Diss. Lund (1948), pp. 1-57.
[1] Titchmarsh, E. C., On conjugate functions, P.L.M.S. 29 (1928), 49–80.Google Scholar
[2] Titchmarsh, E. C., The convergence of certain integrals, P.L.M.S. 24 (1925), 347–58.Google Scholar
[3] Titchmarsh, E. C., Additional note on conjugate functions, J.L.M.S. 4 (1929), 204–6.Google Scholar
[4] Titchmarsh, E. C., Reciprocal formulae for séries and integrals, M.Z. 25 (1926), 321–47.Google Scholar
[5] Titchmarsh, E. C., A theorem on Lebesgue integrals, J.L.M.S. 2 (1927), 36–7.Google Scholar
[6] Titchmarsh, E. C., A contribution to the theory of Fourier transforms, P.L.M.S. 23 (1924), 279–89.Google Scholar
[7] Titchmarsh, E. C., The order of magnitude of the coefficients in a generalized Fourier séries, P.L.M.S. 22 (1925), xxiv-xxvi.Google Scholar
[1] Toeplitz, O., Über allgemeine lineare Mittelbildungen, Prace Matematyczno-Fizyczne, 22 (1911), 113–19.Google Scholar
[2] Toeplitz, O., Über die Fouriersche Entwickelungen positiver Funktionen, R.P. 32 (1911), 191–2.Google Scholar
[3] Toeplitz, O., Zur Theorie der quadratischen und bilinearen Formen von unendlich vielen Vercinderlichen (I), M.A. 70 (1911), 351–76.Google Scholar
[1] Ttjmarkin, G. C., On uniform convergence of certain sequences of functions (in Russian), Doklady, 105 (1955), 1151–4.Google Scholar
[1] TURAN, P., Über die partielle Summen der Fourierreihen, J.L.M.S. 13 (1938), 278–82.Google Scholar
[1] Ulyanov, P. L., Application of A -integration to a class of trigonometric séries, Sbornik, 35 (1954), 469–90.Google Scholar
[1] De La Vallée-Poussin, Ch. J., Sur l'unicité du développement trigonométrique, Bull, de l'Acad. Royale de Belgique (1912), pp. 702–18.Google Scholar
[2] de la Vallée-Poussin, Ch. J., Sur l'approximation des fonctions d'une variable reelle et leurs derivees par les polynomes et les suites limitees de Fourier, Bull, de l'Acad. Royale de Belgique (1908), pp. 193-254.Google Scholar
[3] de la Vallée-Poussin, Ch. J., Sur la convergence des formules d'interpolation entre ordonnees equidistantes, Bull, de l'Acad. Royale de Belgique (1908), pp. 319-410.Google Scholar
[4] de la Valleé-Poussin, Ch. J., Extension de la methode du balayage de Poincare et probleme de Dirichlet, Ann. de l'Institut H. Poincare, 2 (1932), 169–232.Google Scholar
[1] Verblunsky, S., On the theory of trigonometric séries, (I)P.L.M.S. 34 (1932), 441–56; (II), ibid. 457-91; (III), ibid. 526-60; (IV), ibid. 35 (1933), 445–87; (V), P.M. 21 (1933), 168–210.Google Scholar
[2] Verblunsky, S., Note on summable trigonometric séries, J.L.M.S. 6 (1931), 106–12.Google Scholar
[3] Verblunsky, S., Fourier constants and Lebesgue classes, P.L.M.S. 39 (1935), 1–31.Google Scholar
[4] Verblunsky, S., The relation between Riemann's method of summation and Cesáro's, Proc. Camb. Phil. Soc. 26 (1930), 34–42.Google Scholar
[1] Walsh, J. L., A closed set of normal orthogonal functions, A.J.M. 55 (1923), 5–24.Google Scholar
[1] Wang, F U Traing, Strong summability of Fourier séries, Duke J. 12 (1945), 77–87.Google Scholar
[1] Waraszkiewicz, Z., Sur un théorème de M. Zygmund, B.A.P. (1929), pp. 275–9.Google Scholar
[1] Warschawski, S., Über einige Kongvergenzsätze aus der Theorie der konformen Abbildung, Gottinger Nachrichten (1930), pp. 344–69.Google Scholar
[1] Weiss, G., A note on Orlicz spaces, Portugaliae Mat. 15 (1956), 35–47.Google Scholar
[2] Weiss, G., An interpolation theorem for sublinear operations on Hp spaces, Proc. A.M.S. 8 (1957), 92–9.Google Scholar
[1] Weiss, Mary, On the law of the iterated logarithm for lacunary trigonometric séries, T.A.M.S. (1959).
[2] Weiss, Mary, On séries of Hardy and Littlewood, T.A.M.S. (1959).
[3] Weiss, Mary, On a problem of Littlewood, J.L.M.S. 34 (1959).Google Scholar
[1] Weyl, H., Bemerkungen zum Begriff der Differentialquotienten gebrochener Ordnung, Vierteljahrschrift d. Naturforscher Gesellschajt in Zurich, 62 (1917), 296–302.Google Scholar
[2] Weyl, H., Über die Gleichverteilung von Zahlen mod. Eins, M.A. 11 (1916), 313–52.Google Scholar
[1] Wielandt, H., Zur Umkehrung des Abelschen Stetigkeitssatzes, M.Z. 56 (1952), 206–7.Google Scholar
[1] Wiener, N., The quadratic variation of a function and its Fourier coefficients, Massachicsetts J. of Math. 3 (1924), 72–94.Google Scholar
[2] Wiener, N., A class of gap theorems, Annali di Pisa, 3 (1934), 367–72.Google Scholar
[3] Wiener, N., Taüberian theorems, Ann. Math. 33 (1932), 1–100.Google Scholar
[4] Wiener, N., Generalized harmonic analysis, A.M. 55 (1930), 117–258.Google Scholar
[5] Wiener, N., On the representation of functions by trigonometrical integrals, M.Z. 24 (1925), 575–616.Google Scholar
[1] Wiener, N. and Wintner, A., On singular distributions, J. Math. Physics, 17 (1938), 233–46.CrossRefGoogle Scholar
[2] Wiener, N. and Wintner, A., Fourier-Stieltjes transforms and singular infinite convolutions, A.J.M. 40 (1938) 513–22.Google Scholar
[1] Wilton, J. R., An approximate functional equation of a simple type: Applications to a certain trigonometrical séries, J.L.M.S. 9 (1934), 247–54.Google Scholar
[1] Wolf, F., On summable trigonometrical séries, P.L.M.S. 45 (1939), 328–56.Google Scholar
[2] Wolf, F., The Poisson integral. A study in the uniqueness of harmonic functions, A.M. 74 (1941), 65–100.Google Scholar
[3] Wolf, F., Contributions to the theory of summable trigonometric integrals, Univ. of California, Publ. Math. 1 (1947), 159–227.Google Scholar
[1] Yano, S., An extrapolation theorem, J. Math. Soc. Japan, 3 (1951), 296–305.CrossRefGoogle Scholar
[1] Young, G. C. and W. H., On the theorem of Riesz and Fischer, Q.J. 44 (1913), 49–88.Google Scholar
[1] Young, L. C., On an inequality of Marcel Riesz, Ann. Math. 40 (1939), 367–74.Google Scholar
[1] Young, W. H., On the integration of Fourier séries, P.L.M.S. 9 (1911), 449–62.Google Scholar
[2] Young, W. H., Sur la généralisation du théorème de Parseval, C.R. 155 (1912), 30–3.Google Scholar
[3] Young, W. H., On the multiplication of successions of Fourier constants, Proc. Roy. Soc. A, 87 (1912), 331–9.CrossRefGoogle Scholar
[4] Young, W. H., On the determination of the summability of a function by means of its Fourier constants, P.L.M.S. 12 (1913), 71–88.Google Scholar
[5] Young, W. H., Konvergenzbedingungen fiir die verwandte Reihe einer Fourierschen Reihe, Miinchener Sitzungsberichte, 41 (1911), 361–71.Google Scholar
[6] Young, W. H., On the mode of oscillation of a Fourier séries and of its allied séries, P.L.M.S. 12 (1913), 433–52.Google Scholar
[7] Young, W. H., On successions with subsequences converging to an integral, P.L.M.S. 24 (1926), 1–20.Google Scholar
[8] Young, W. H., On the Fourier séries of bounded functions, P.L.M.S. 12 (1913), 41–70.Google Scholar
[9] Young, W. H., On the ordinary convergence of restricted Fourier séries, Proc. Roy. Soc. A, 93 (1917), 276–92.CrossRefGoogle Scholar
[10] Young, W. H., On restricted Fourier séries and the convergence of power séries, P.L.M.S. 17 (1918), 353–66.Google Scholar
[11] Young, W. H., On the connexion between Legendre séries and Fourier séries, P.L.M.S. 18 (1920), 141–62.Google Scholar
[1] Zaanen, A. C., On a certain class of Banach spaces, Ann. Math. 47 (1946), 657–66.Google Scholar
[1] Zalcwasser, Z., Sur le phénomène de Gibbs dans la théorie des séries de Fourier des fonctions continues, F.M. 12 (1928), 126–51.Google Scholar
[1] Zamansky, M., Classes de saturation de certains procédés d'approximation des séries de Fourier, A.E.N.S. 66 (1949), 19–93.Google Scholar
[2] Zamansky, M., Classes de saturation des procedes de sommation des séries de Fourier, A.E,N.S. 67 (1950), 161–98.Google Scholar
[3] Zamansky, M., Sur F approximation des fonctions continues, C.R. 228 (1949), 460–1.Google Scholar
[1] Zarantonello, E. H., On trigonometric interpolation, Proc. A.M.S. 3 (1952), 770–82.Google Scholar
[1] Zeller, K., Über Konvergenzmengen der Fourierreihen, Archiv der Math. 6 (1955), 335–40.Google Scholar
[1] Zygmund, A., Smooth functions, Duke J. 12 (1945), 47–76.Google Scholar
[2] Zygmund, A., Sur la sommation des séries conjuguees aux séries de Fourier, B.A.P. (1924), pp. 251–8.
[3] Zygmund, A., On the degree of approximation of functions by their Fejer means, B.A.M.S. 51 (1945), 274–8.Google Scholar
[4] Zygmund, A., Sur les fonctions conjuguees, F.M. 13 (1929), 284–303; Corrigenda, ibid. 18 (1932), 312.Google Scholar
[5] Zygmund, A., Some points in the theory of trigonometric and power séries, T.A.M.S. 36 (1934), 586–617.Google Scholar
[6] Zygmund, A., Sur un théorème de M. Fekete, B.A.P. (1927), pp. 343–7.Google Scholar
[7] Zygmund, A., On a theorem of Hadamard, Ann. de la Soc. Polonaise de Math. 21 (1948), 52–70; Errata, ibid. 357-9.Google Scholar
[8] Zygmund, A., On the convergence of lacunary trigonometric séries, F.M. 16 (1930), 90–107.Google Scholar
[9] Zygmund, A., On lacunary trigonometric séries, T.A.M.S. 34 (1932), 435–46.Google Scholar
[10] Zygmund, A., A remark on conjugate séries, P.L.M.S. 34 (1932), 392–400.Google Scholar
[11] Zygmund, A., Sur la convergence absolue des séries de Fourier, J.L.M.S. 3 (1928), 194–6.Google Scholar
[12] Zygmund, A., Quelques théorèmes sur les séries trigonométriques et celles de puissances, S.M. 3 (1931), 77–91.Google Scholar
[13] Zygmund, A., On a theorem of Littlewood, Summa Brasiliensis Mathematicae, 2 (1949), Fasc. 5.Google Scholar
[14] Zygmund, A., Sur la theorie riemannienne des séries trigonométriques, M.Z. 24 (1926), 47–104.Google Scholar
[15] Zygmund, A., Sur un théorènie de M. Fejér, Bull, du Séminaire Math, de l'Université de Wilno, 2 (1939), 3–12.Google Scholar
[16] Zygmund, A., An example in Fourier séries, S.M. 10 (1948), 113–19.Google Scholar
[17] Zygmund, A., Note on the formal multiplication of trigonometrical séries, Bull, du Séminaire Math. de VUniv. de Wilno, 2 (1939), 62–6.Google Scholar
[18] Zygmund, A., Sur la théorie riemannienne de certains systémes orthogonaux, (I)S.M. 2 (1930), 97–170; (II) Brace Matematyczno-Fizyczne, 39 (1932), 73–117.Google Scholar
[19] Zygmund, A., Sur les séries trigonométriques sommables par le procede de Poisson, M.Z. 25 (1926), 274–90.Google Scholar
[20] Zygmund, A., On certain integrals, T.A.M.S. 55 (1944), 170–204.Google Scholar
[21] Zygmund, A., On the convergence and summability of power séries on the circle of convergence, (I), F.M. 30 (1928), 170–96; (II), P.L.M.S. 47 (1941), 326–50.Google Scholar
[22] Zygmund, A., Sur un théorème de M. Gronwall, B.A.P. (1925), pp. 207–17.Google Scholar
[23] Zygmund, A., Sur Tapplication de la premiere moyenne arithmetique, F.M. 10 (1926), 356–62.Google Scholar
[24] Zygmund, A., On the summability of multiple Fourier séries, A.J.M. 69 (1947), 836–50.Google Scholar
[25] Zygmund, A., On the boundary values of functions of several complex variables, F.M. 36 (1949), 207–35.Google Scholar
[26] Zygmund, A., On the differentiability of multiple integrals, F.M. 23 (1934), 143–9.Google Scholar
[27] Zygmund, A., On the Littlewood-Paley function g*(θ), Proc. Nat. Acad. U.S.A. 42 (1956), 208–12.Google Scholar
[28] Zygmund, A., On a theorem of Marcinkiewicz concerning interpolation of operations, Journal de Math. 35 (1956), 223–48.Google Scholar
[29] Zygmund, A., A remark on Fourier transforms, Proc. Camb. Phil. Soc. 32 (1936).Google Scholar
[30] Zygmund, A., Über die Beziehungen der Eindeutigkeitsfragen in der Theorien der trigonometrischen Reihen und Integrale, M.A. 99 (1928), 562–89.Google Scholar
[31] Zygmund, A., Trigonometric integrals, Ann. Math. 48 (1947), 393–440.Google Scholar

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  • References
  • A. Zygmund
  • Foreword by Robert Fefferman, University of Chicago
  • Book: Trigonometric Series
  • Online publication: 05 February 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781316036587.025
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  • References
  • A. Zygmund
  • Foreword by Robert Fefferman, University of Chicago
  • Book: Trigonometric Series
  • Online publication: 05 February 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781316036587.025
Available formats
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  • References
  • A. Zygmund
  • Foreword by Robert Fefferman, University of Chicago
  • Book: Trigonometric Series
  • Online publication: 05 February 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781316036587.025
Available formats
×