References

Pertti Mattila

doi:10.1017/CBO9781316227619.027

B., Barany and M., Rams [2014] Dimension of slices of Sierpinski-like carpets, J. Fractal Geom. 1, 273–294.Google Scholar

B., Barceló [1985] On the restriction of the Fourier transform to a conical surface, Trans. Amer. Math. Soc. 292, 321–333.Google Scholar

J. A., Barceló, J., Bennett, A., Carbery and K. M., Rogers [2011] On the dimension of divergence sets of dispersive equations, Math. Ann. 349, 599–622.Google Scholar

J. A., Barceló, J., Bennett, A., Carbery, A., Ruiz and M. C., Vilela [2007] Some special solutions of the Schrödinger equation, Indiana Univ. Math. J. 56, 1581–1593.Google Scholar

M., Bateman [2009] Kakeya sets and directional maximal operators in the plane, Duke Math. J. 147, 55–77.Google Scholar

M., Bateman and N. H., Katz [2008] Kakeya sets in Cantor directions, Math. Res. Lett. 15, 73–81.Google Scholar

M., Bateman and A., Volberg [2010] An estimate from below for the Buffon needle probability of the four-corner Cantor set, Math. Res. Lett. 17, 959–967.Google Scholar

W., Beckner, A., Carbery, S., Semmes and F., Soria [1989] A note on restriction of the Fourier transform to spheres, Bull. London Math. Soc. 21, 394–398.Google Scholar

I., Benjamini and Y., Peres [1991] On the Hausdorff dimension of fibres, Israel J. Math. 74, 267–279.Google Scholar

J., Bennett [2014] Aspects of multilinear harmonic analysis related to transversality, Harmonic analysis and partial differential equations, Contemporary Math. 612, 1–28.Google Scholar

J., Bennett, T., Carbery and T., Tao [2006] On the multilinear restriction and Kakeya conjectures, Acta Math. 196, 261–302.Google Scholar

J., Bennett and K. M., Rogers [2012] On the size of divergence sets for the Schrödinger equation with radial data, Indiana Univ. Math. J. 61, 1–13.Google Scholar

J., Bennett and A., Vargas [2003] Randomised circular means of Fourier transforms of measures, Proc. Amer. Math. Soc. 131, 117–127.Google Scholar

M., Bennett, A., Iosevich and K., Taylor [2014] Finite chains inside thin subsets of Rd, arXiv:1409.2581.

A. S., Besicovitch [1919] Sur deux questions d'intégrabilité des fonctions, J. Soc. Phys- Math. (Perm) 2, 105–123.Google Scholar

A. S., Besicovitch [1928] On Kakeya's problem and a similar one, Math. Zeitschrift 27, 312–320.Google Scholar

A. S., Besicovitch [1964] On fundamental geometric properties of plane line–sets, J. London Math. Soc. 39, 441–448.Google Scholar

D., Betsakos [2004] Symmetrization, symmetric stable processes, and Riesz capacities, Trans. Amer. Math. Soc. 356, 735–755.Google Scholar

C. J., Bishop and Y., Peres [2016] Fractal Sets in Probability and Analysis, Cambridge University Press.

C., Bluhm [1996] Random recursive construction of Salem sets, Ark. Mat. 34, 51–63.Google Scholar

C., Bluhm [1998] On a theorem of Kaufman: Cantor-type construction of linear fractal Salem sets, Ark. Mat. 36, 307–316.Google Scholar

M., Bond, I., Łaba and A., Volberg [2014] Buffon's needle estimates for rational product Cantor sets, Amer. J. Math. 136, 357–391.Google Scholar

M., Bond, I., Łaba and J., Zhai [2013] Quantitative visibility estimates for unrectifiable sets in the plane, to appear in Trans. Amer. Math. Soc., arXiv:1306.5469.

M., Bond and A., Volberg [2010] Buffon needle lands in ε-neighborhood of a 1- dimensional Sierpinski gasket with probability at most j log εjc, C. R. Math. Acad. Sci. Paris 348, 653–656.Google Scholar

M., Bond [2011] Circular Favard length of the four-corner Cantor set, J. Geom. Anal. 21, 40–55.Google Scholar

M., Bond [2012] Buffon's needle landing near Besicovitch irregular self-similar sets, Indiana Univ. Math. J. 61, 2085–2019.Google Scholar

J., Bourgain [1986] Averages in the plane over convex curves and maximal operators, J. Anal. Math. 47, 69–85.Google Scholar

J., Bourgain [1991a] Besicovitch type maximal operators and applications to Fourier analysis, Geom. Funct. Anal. 1, 147–187.Google Scholar

J., Bourgain [1991b] Lp-estimates for oscillatory integrals in several variables, Geom. Funct. Anal. 1, 321–374.Google Scholar

J., Bourgain [1993] On the distribution of Dirichlet sums, J. Anal. Math. 60, 21–32.Google Scholar

J., Bourgain [1994] Hausdorff dimension and distance sets, Israel J. Math. 87, 193–201.Google Scholar

J., Bourgain [1995] Some new estimates on oscillatory integrals, in Essays on Fourier Analysis in Honor of Elias M. Stein, Princeton University Press, 83–112.

J., Bourgain[1999] On the dimension of Kakeya sets and related maximal inequalities, Geom. Funct. Anal. 9, 256–282.Google Scholar

J., Bourgain [2003] On the Erdős–Volkmann and Katz–Tao ring conjectures, Geom. Funct. Anal. 13, 334–365.Google Scholar

J., Bourgain [2010] The discretized sum-product and projection theorems, J. Anal. Math. 112, 193–236.Google Scholar

J., Bourgain [2013] On the Schrödinger maximal function in higher dimension, Proc. Steklov Inst. Math. 280, 46–60.Google Scholar

J., Bourgain and L., Guth [2011] Bounds on oscillatory integral operators based on multilinear estimates, Geom. Funct. Anal. 21, 1239–1235.Google Scholar

J., Bourgain, N. H., Katz and T., Tao [2004] A sum-product estimate in finite fields, and applications, Geom. Funct. Anal. 14, 27–57.Google Scholar

G., Brown and W., Moran [1974] On orthogonality for Riesz products, Proc. Cambridge Philos. Soc. 76, 173–181.Google Scholar

A. M., Bruckner, J. B., Bruckner and B. S., Thomson [1997] Real Analysis, Prentice Hall.

A., Carbery [1992] Restriction implies Bochner–Riesz for paraboloids, Math. Proc. Cambridge Philos. Soc. 111, 525–529.Google Scholar

A., Carbery [2004] A multilinear generalisation of the Cauchy-Schwarz inequality, Proc. Amer. Math. Soc. 132, 3141–3152.Google Scholar

A., Carbery [2009] Large sets with limited tube occupancy, J. Lond. Math. Soc. (2) 79, 529–543.Google Scholar

A., Carbery, F., Soria and A., Vargas [2007] Localisation and weighted inequalities for spherical Fourier means, J. Anal. Math. 103, 133–156.Google Scholar

A., Carbery and S. I., Valdimarsson [2013] The endpoint multilinear Kakeya theorem via the Borsuk–Ulam theorem, J. Funct. Anal. 264, 1643–1663.Google Scholar

L., Carleson [1967] Selected Problems on Exceptional Sets, Van Nostrand.

L., Carleson [1980] Some analytic problems related to statistical mechanics, in Euclidean Harmonic Analysis, Lecture Notes in Math. 779, Springer-Verlag, 5–45.Google Scholar

L., Carleson and P., Sjölin [1972] Oscillatory integrals and a multiplier problem for the disc, Studia Math. 44, 287–299.Google Scholar

V., Chan, I., Łaba and M., Pramanik [2013] Finite configurations in sparse sets, to appear in J. Anal. Math., arXiv:1307.1174.

J., Chapman, M. B., Erdoğan, D., Hart, A., Iosevich and D., Koh [2012] Pinned distance sets, k-simplices,Wolff 's exponent in finite fields and sum-product estimates, Math. Z. 271, 63–93.Google Scholar

X., Chen [2014a] Sets of Salem type and sharpness of the L2-Fourier restriction theorem, to appear in Trans. Amer. Math. Soc., arXiv:1305.5584.

X., Chen [2014b] A Fourier restriction theorem based on convolution powers, Proc. Amer. Math. Soc. 142, 3897–3901.Google Scholar

M., Christ [1984] Estimates for the k-plane tranforms, Indiana Univ. Math. J. 33, 891–910.Google Scholar

M., Christ, J., Duoandikoetxea and J. L. Rubio de, Francia [1986] Maximal operators related to the Radon transform and the Calderón-Zygmund method of rotations, Duke Math. J. 53, 189–209.Google Scholar

A., Córdoba [1977] The Kakeya maximal function and the spherical summation of multipliers, Amer. J. Math. 99, 1–22.Google Scholar

B. E. J., Dahlberg and C. E., Kenig [1982] A note on the almost everywhere behavior of solutions to the Schrödinger equation, in Harmonic Analysis, Lecture Notes in Math. 908, Springer-Verlag, 205–209.Google Scholar

G., David and S., Semmes [1993] Analysis of and on Uniformly Rectifiable Sets, Surveys and Monographs 38, Amer. Math. Soc.

R. O., Davies [1952a] On accessibility of plane sets and differentation of functions of two real variables, Proc. Cambridge Philos. Soc. 48, 215–232.Google Scholar

R. O., Davies [1952b] Subsets of finite measure in analytic sets, Indag. Math. 14, 488–489.Google Scholar

R. O., Davies [1971] Some remarks on the Kakeya problem, Proc. Cambridge Philos. Soc. 69, 417–421.Google Scholar

C., Demeter [2012] L2 bounds for a Kakeya type maximal operator in ℝ3, Bull. London Math. Soc. 44, 716–728.Google Scholar

S., Dendrinos and D., Müller [2013] Uniform estimates for the local restriction of the Fourier transform to curves, Trans. Amer.Math. Soc. 365, 3477–3492.Google Scholar

C., Donoven and K.J., Falconer [2014] Codimension formulae for the intersection of fractal subsets of Cantor spaces, arXiv:1409.8070.

S.W., Drury [1983] Lp estimates for the X-ray transform, Illinois J. Math. 27, 125–129.Google Scholar

J., Duoandikoetxea [2001] Fourier Analysis, Graduate Studies in Mathematics Volume 29, American Mathematical Society.

Z., Dvir [2009] On the size of Kakeya sets in finite fields, J. Amer. Math. Soc. 22, 1093–1097.Google Scholar

Z., Dvir and A., Wigderson [2011] Kakeya sets, new mergers, and old extractors, SIAM J. Comput. 40, 778–792.Google Scholar

G. A., Edgar and C., Miller [2003] Borel subrings of the reals, Proc. Amer. Math. Soc. 131, 1121–1129.Google Scholar

F., Ekström, T., Persson, J., Schmeling [2015] On the Fourier dimension and a modification, to appear in J. Fractal Geom., arXiv:1406.1480.

F., Ekström [2014] The Fourier dimension is not finitely stable, arXiv:1410.3420.

M., Elekes, T., Keleti and A., Máthé [2010] Self-similar and self-affine sets: measure of the intersection of two copies, Ergodic Theory Dynam. Systems 30, 399–440.Google Scholar

J. S., Ellenberg, R., Oberlin and T., Tao [2010] The Kakeya set and maximal conjectures for algebraic varieties over finite fields, Mathematika 56, 1–25.Google Scholar

M. B., Erdoğan [2004] A note on the Fourier transform of fractal measures, Math. Res. Lett. 11, 299–313.Google Scholar

M. B., Erdoğan [2005] A bilinear Fourier extension problem and applications to the distance set problem, Int. Math. Res. Not. 23, 1411–1425.Google Scholar

M. B., Erdoğan [2006] On Falconer's distance set conjecture, Rev. Mat. Iberoam. 22, 649–662.Google Scholar

M. B., Erdoğan, D., Hart and A., Iosevich [2013] Multi-parameter projection theorems with applications to sums-products and finite point configurations in the Euclidean setting, in RecentAdvances in HarmonicAnalysis and Applications, Springer Proc. Math. Stat., 25, Springer, 93–103.Google Scholar

M. B., Erdoğan and D. M., Oberlin [2013] Restricting Fourier transforms of measures to curves in ℝ2, Canad. Math. Bull. 56, 326–336.Google Scholar

P., Erdős [1939] On a family of symmetric Bernoulli convolutions, Amer. J. Math. 61, 974–976.Google Scholar

P., Erdős [1940] On the smoothness properties of a family of Bernoulli convolutions, Amer. J. Math. 62, 180–186.Google Scholar

P., Erdős [1946] On sets of distances of n points, Amer. Math. Monthly 53, 248–250.Google Scholar

P., Erdős and B., Volkmann [1966] Additive Gruppen mit vorgegebener Hausdorffscher Dimension, J. Reine Angew. Math. 221, 203–208.Google Scholar

S., Eswarathasan, A., Iosevich and K., Taylor [2011] Fourier integral operators, fractal sets, and the regular value theorem, Adv. Math. 228, 2385–2402.Google Scholar

S., Eswarathasan [2013] Intersections of sets and Fourier analysis, to appear in J. Anal. Math.

L. C., Evans [1998] Partial Differential Equations, Graduate Studies in Mathematics 19, Amer. Math. Soc.

L. C., Evans and R. F., Gariepy [1992] Measure Theory and Fine Properties of Functions, CRC Press.

K. J., Falconer [1980a] Continuity properties of k-plane integrals and Besicovitch sets, Math. Proc. Cambridge Philos. Soc. 87, 221–226.Google Scholar

K. J., Falconer [1980b] Sections of sets of zero Lebesgue measure, Mathematika 27, 90–96.Google Scholar

K. J., Falconer [1982] Hausdorff dimension and the exceptional set of projections, Mathematika 29, 109–115.Google Scholar

K. J., Falconer [1984] Rings of fractional dimension, Mathematika 31, 25–27.Google Scholar

K. J., Falconer [1985a] Geometry of Fractal Sets, Cambridge University Press.

K. J., Falconer [1985b] On the Hausdorff dimension of distance sets, Mathematika 32, 206–212.Google Scholar

K. J., Falconer [1986] Sets with prescribed projections and Nikodym sets, Proc. London Math. Soc. (3) 53, 48–64.Google Scholar

K. J., Falconer [1990] Fractal Geometry: Mathematical Foundations and Applications, John Wiley and Sons.

K. J., Falconer [1997] Techniques in Fractal Geometry, John Wiley and Sons.

K. J., Falconer [2005] Dimensions of intersections and distance sets for polyhedral norms, Real Anal. Exchange 30, 719–726.Google Scholar

K. J., Falconer, J., Fraser and X., Jin [2014] Sixty years of fractal projections, arXiv:1411.3156.

K. J., Falconer and J. D., Howroyd [1996] Projection theorems for box and packing dimensions, Math. Proc. Cambridge Philos. Soc. 119, 287–295.Google Scholar

K. J., Falconer and J. D., Howroyd [1997] Packing dimensions of projections and dimension profiles, Math. Proc. Cambridge Philos. Soc. 121, 269–286.Google Scholar

K. J., Falconer and X., Jin [2014a] Exact dimensionality and projections of random self-similar measures and sets, J. London Math. Soc. 90, 388–412.Google Scholar

K. J., Falconer and X., Jin [2014b] Dimension conservation for self-similar sets and fractal percolation, arXiv:1409.1882.

K. J., Falconer and P., Mattila [1996] The packing dimension of projections and sections of measures, Math. Proc. Cambridge Philos. Soc. 119, 695–713.Google Scholar

K. J., Falconer and P., Mattila [2015] Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes, arXiv:1503.01284.

K. J., Falconer and T., O'Neil [1999] Convolutions and the geometry of multifractal measures, Math. Nachr. 204, 61–82.Google Scholar

A.-H., Fan and X., Zhang [2009] Some properties of Riesz products on the ring of p-adic integers, J. Fourier Anal. Appl. 15, 521–552.Google Scholar

A., Farkas [2014] Projections and other images of self-similar sets with no separation condition, arXiv:1307.2841.

K., Fässler and R., Hovila [2014] Improved Hausdorff dimension estimate for vertical projections in the Heisenberg group, Ann. Scuola Norm. Sup. Pisa.

K., Fässler and T., Orponen [2013] Constancy results for special families of projections, Math. Proc. Cambridge Philos. Soc. 154, 549–568.Google Scholar

K., Fässler and T., Orponen [2014] On restricted families of projections in ℝ3, Proc. London Math. Soc. (3) 109, 353–381.Google Scholar

H., Federer [1969] Geometric Measure Theory, Springer-Verlag.

C., Fefferman [1970] Inequalities for strongly singular convolution operators, Acta Math. 124, 9–36.Google Scholar

C., Fefferman [1971] The multiplier problem for the ball, Ann. of Math. (2) 94, 330–336.Google Scholar

A., Ferguson, J., Fraser, and T., Sahlsten [2015] Scaling scenery of (m,n) invariant measures, Adv. Math. 268, 564–602.Google Scholar

A., Ferguson, T., Jordan and P., Shmerkin [2010] The Hausdorff dimension of the projections of self-affine carpets, Fund. Math. 209, 193–213.Google Scholar

J., Fraser, E. J., Olson and J. C., Robinson [2014] Some results in support of the Kakeya Conjecture, arXiv:1407.6689.

J., Fraser, T., Orponen and T., Sahlsten [2014] On Fourier analytic properties of graphs, Int. Math. Res. Not. 10, 2730–2745.Google Scholar

D., Freedman and J., Pitman [1990] A measure which is singular and uniformly locally uniform, Proc. Amer. Math. Soc. 108, 371–381.Google Scholar

H., Furstenberg [1970] Intersections of Cantor sets and transversality of semigroups, Problems in Analysis, Sympos. Salomon Bochner, Princeton University, Princeton, N.J. 1969, Princeton University Press, 41–59.

H., Furstenberg [2008] Ergodic fractal measures and dimension conservation, Ergodic Theory Dynam. Systems 28, 405–422.Google Scholar

J., Garibaldi, A., Iosevich and S., Senger [2011] The Erdős distance problem, Student Mathematical Library, 56, American Mathematical Society.

L., Grafakos [2008] Classical Fourier Analysis, Springer-Verlag.

L., Grafakos [2009] Modern Fourier Analysis, Springer-Verlag.

L., Grafakos, A., Greenleaf, A., Iosevich and E., Palsson [2012] Multilinear generalized Radon transforms and point configurations, to apper in Forum Math., arXiv:1204.4429.

C. C., Graham and O. C., McGehee [1970] Essays in Commutative Harmonic Analysis, Springer-Verlag.

A., Greenleaf and A., Iosevich [2012] On triangles determined by subsets of the Euclidean plane, the associated bilinear operators and applications to discrete geometry, Anal. PDE 5, 397–409.Google Scholar

A., Greenleaf, A., Iosevich, B., Liu and E., Palsson [2013] A group-theoretic viewpoint on Erdos-Falconer problems and theMattila integral, to appear in Rev. Mat. Iberoam., arXiv:1306.3598.

A., Greenleaf, A., Iosevich and M., Mourgoglou [2011] On volumes determined by subsets of Euclidean space, arXiv:1110.6790.

A., Greenleaf, A., Iosevich and M., Pramanik [2014] On necklaces inside thin subsets of ℝd, arXiv:1409.2588.

M., Gromov and L., Guth [2012] Generalizations of the Kolmogorov–Barzdin embedding estimates, Duke Math. J. 161, 2549–2603.Google Scholar

L., Guth [2007] The width-volume inequality, Geom. Funct. Anal. 17, 1139–1179.Google Scholar

L., Guth [2010] The endpoint case of the Bennett–Carbery–Taomultilinear Kakeya conjecture, Acta Math. 205, 263–286.Google Scholar

L., Guth [2014] A restriction estimate using polynomial partitioning, arXiv:1407. 1916.

L., Guth [2015] A short proof of the multilinear Kakeya inequality, Math. Proc. Cambridge Philos. Soc. 158, 147–153.Google Scholar

L., Guth and N., Katz [2010] Algebraic methods in discrete analogs of the Kakeya problem, Adv. Math. 225, 2828–2839.Google Scholar

L., Guth and N., Katz [2015] On the Erdős distinct distance problem in the plane, Ann. of Math. (2) 181, 155–190.Google Scholar

M., de Guzmán [1975] Differentiation of Integrals in ℝn, Lecture Notes in Mathematics 481, Springer-Verlag.

M., de Guzmán [1981] Real Variable Methods in Fourier Analysis, North-Holland.

S., Ham and S., Lee [2014] Restriction estimates for space curves with respect to general measures, Adv. Math. 254, 251–279.Google Scholar

K., Hambrook and I., Łaba [2013] On the sharpness of Mockenhaupt's restriction theorem, Geom. Funct. Anal. 23, 1262–1277.Google Scholar

V., Harangi, T., Keleti, G., Kiss, P., Maga, A., Máthé, P., Mattila and B., Strenner [2013] How large dimension guarantees a given angle, Monatshefte für Mathematik 171, 169–187.Google Scholar

K. E., Hare, M., Parasar and M., Roginskaya [2007] A general energy formula, Math. Scand. 101, 29–47.Google Scholar

K. E., Hare and M., Roginskaya [2002] A Fourier series formula for energy of measures with applications to Riesz products, Proc. Amer. Math. Soc. 131, 165–174.Google Scholar

K. E., Hare and M., Roginskaya [2003] Energy of measures on compact Riemannian manifolds, Studia Math. 159, 291–314.Google Scholar

K. E., Hare and M., Roginskaya [2004] The energy of signed measures, Proc. Amer. Math. Soc. 133, 397–406.Google Scholar

D., Hart, A., Iosevich, D., Koh and M., Rudnev [2011] Averages over hyperplanes, sumproduct theory in vector spaces over finite fields and the Erdős-Falconer distance conjecture, Trans. Amer. Math. Soc. 363, 3255–3275.Google Scholar

V., Havin and B., Jöricke [1995] The Uncertainty Principle in Harmonic Analysis, Springer-Verlag.

J., Hawkes [1975] Some algebraic properties of small sets, Quart. J. Math. 26, 195–201.Google Scholar

D. R., Heath-Brown [1987] Integer sets containing no arithmetic progressions, J. London Math. Soc. (2) 35, 385–394.Google Scholar

Y., Heo, F., Nazarov and A., Seeger [2011] Radial Fourier multipliers in high dimensions, Acta Math. 206, 55–92.Google Scholar

M., Hochman [2014] On self-similar sets with overlaps and inverse theorems for entropy, Ann. of Math. (2) 180, 773–822.Google Scholar

M., Hochman and P., Shmerkin [2012] Local entropy averages and projections of fractal measures, Ann. of Math. (2) 175, 1001–1059.Google Scholar

S., Hofmann and A., Iosevich [2005] Circular averages and Falconer/Erdős distance conjecture in the plane for random metrics, Proc. Amer. Math. Soc 133, 133–143.Google Scholar

S., Hofmann, J. M., Martell and I., Uriarte-Tuero [2014] Uniform rectifiability and harmonic measure II: Poisson kernels in Lp imply uniform rectifiability, Duke Math. J. 163, 1601–1654.Google Scholar

S., Hofmann and M., Mitrea and Taylor, Mitrea [2010] Singular integrals and elliptic boundary problems on regular Semmes–Kenig–Toro domains, Int. Math. Res. Not. 14, 2567–2865.Google Scholar

L., Hörmander [1973] Oscillatory integrals and multipliers on FLp, Ark. Math. 11, 1–11.Google Scholar

R., Hovila [2014] Transversality of isotropic projections, unrectifiability, and Heisenberg groups, Rev. Math. Iberoam. 30, 463–476.Google Scholar

R., Hovila, E., Järvenpää, M., Järvenpää and F., Ledrappier [2012a] Besicovitch-Federer projection theorem and geodesic flows on Riemann surfaces, Geom. Dedicata 161, 51–61.Google Scholar

R., Hovila, E., Järvenpää, M., Järvenpää and F., Ledrappier [2012b] Singularity of projections of 2-dimensional measures invariant under the geodesic flow, Comm. Math. Phys. 312, 127–136.Google Scholar

J. E., Hutchinson [1981] Fractals and self-similarity, Indiana Univ. Math. J. 30, 713–747.Google Scholar

A., Iosevich [2000] Kakeya lectures, www.math.rochester.edu/people/faculty/iosevich/ expositorypapers.html.

A., Iosevich [2001] Curvature, Combinatorics, and the Fourier Transform, Notices Amer. Math. Soc. 48(6), 577–583.Google Scholar

A., Iosevich and I., Łaba [2004] Distance sets of well-distributed planar point sets, Discrete Comput. Geom. 31, 243–250.Google Scholar

A., Iosevich and I., Łaba [2005] K-distance sets, Falconer conjecture and discrete analogs, Integers 5, 11 pp.Google Scholar

A., Iosevich, M., Mourgoglou and E., Palsson [2011] On angles determined by fractal subsets of the Euclidean space via Sobolev bounds for bi-linear operators, to appear in Math. Res. Lett., arXiv:1110.6792.

A., Iosevich, M., Mourgoglou and S., Senger [2012] On sets of directions determined by subsets of ℝd, J. Anal. Math. 116, 355–369.Google Scholar

A., Iosevich, M., Mourgoglou and K., Taylor [2012] On the Mattila-Sjölin theorem for distance sets, Ann. Acad. Sci Fenn. Ser. A I Math. 37, 557–562.Google Scholar

A., Iosevich and M., Rudnev [2005] Non-isotropic distance measures for lattice generated sets, Publ. Mat. 49, 225–247.Google Scholar

A., Iosevich and M., Rudnev [2007a] Distance measures for well-distributed sets, Discrete Comput. Geom. 38, 61–80.Google Scholar

A., Iosevich and M., Rudnev [2007b] The Mattila integral associated with sign indefinite measures, J. Fourier Anal. Appl. 13, 167–173.Google Scholar

A., Iosevich and M., Rudnev [2007c] Erdős distance problem in vector spaces over finite fields, Trans. Amer. Math. Soc. 359, 6127–6142.Google Scholar

A., Iosevich and M., Rudnev [2009] Freiman theorem, Fourier transform, and additive structure of measures, J. Aust. Math. Soc. 86, 97–109.Google Scholar

A., Iosevich, M., Rudnev and I., Uriarte-Tuero [2014] Theory of dimension for large discrete sets and applications, Math. Model. Nat. Phenom. 9, 148–169.Google Scholar

A., Iosevich, E., Sawyer, K., Taylor and I., Uriarte-Tuero [2014] Measures of polynomial growth and classical convolution inequalities, arXiv:1410.1436.

A., Iosevich and S., Senger [2010] On the sharpness of Falconer's distance set estimate and connections with geometric incidence theory, arXiv:1006.1397.

V., Jarnik [1928] Zur metrischen theorie der diophantischen approximationen, Prace Mat. Fiz., 36(1), 91–106.Google Scholar

V., Jarnik [1931] Über die simultanen diophantischen Approximationen, Mat. Z. 33, 505–543.Google Scholar

E., Järvenpää, M., Järvenpää and T., Keleti [2014] Hausdorff dimension and nondegenerate families of projections, J. Geom. Anal. 24, 2020–2034.Google Scholar

E., Järvenpää, M., Järvenpää, T., Keleti and A., Máthé [2011] Continuously parametrized Besicovitch sets in ℝn, Ann. Acad. Sci. Fenn. Ser. A I Math. 36, 411–421.Google Scholar

E., Järvenpää, M., Järvenpää, F., Ledrappier and M., Leikas [2008] One-dimensional families of projections, Nonlinearity 21, 453–463.Google Scholar

E., Järvenpää, M., Järvenpää and M., Leikas [2005] (Non)regularity of projections of measures invariant under geodesic flow, Comm. Math. Phys. 254, 695–717.Google Scholar

E., Järvenpää, M., Järvenpää and M., Llorente [2004] Local dimensions of sliced measures and stability of packing dimensions of sections of sets, Adv. Math. 183, 127–154.Google Scholar

M., Järvenpää [1994] On the upper Minkowski dimension, the packing dimension, and orthogonal projections, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 99, 1–34.Google Scholar

M., Järvenpää [1997a] Concerning the packing dimension of intersection measures, Math. Proc. Cambridge Philos. Soc. 121, 287–296.Google Scholar

M., Järvenpää [1997b] Packing dimension, intersection measures, and isometries, Math. Proc. Cambridge Philos. Soc. 122, 483–490.Google Scholar

M., Järvenpää and P., Mattila [1998] Hausdorff and packing dimensions and sections of measures, Mathematika 45, 55–77.Google Scholar

T., Jordan and T., Sahlsten [2013] Fourier transforms of Gibbs measures for the Gauss map, to appear in Math. Ann., arXiv:1312.3619.

A., Käenmäki and P., Shmerkin [2009] Overlapping self-affine sets of Kakeya type, Ergodic Theory Dynam. Systems 29, 941–965.Google Scholar

J.-P., Kahane [1969] Trois notes sur les ensembles parfaits linéaires, Enseign. Math. 15, 185–192.Google Scholar

J.-P., Kahane [1970] Sur certains ensembles de Salem, Acta Math. Acad. Sci. Hungar. 21, 87–89.Google Scholar

J.-P., Kahane [1971] Sur la distribution de certaines séries aléatoires, in Colloque de Théories des Nombres (Univ. Bordeaux, Bordeaux 1969), Bull. Soc. Math. France Mém. 25, 119–122.Google Scholar

J.-P., Kahane [1985] Some Random Series of Functions, Cambridge University Press, second edition, first published 1968.

J.-P., Kahane [1986] Sur la dimension des intersections, in Aspects of Mathematics and Applications, North-Holland Math. Library, 34, 419–430.Google Scholar

J.-P., Kahane [2010] Jacques Peyriére et les produits de Riesz, arXiv:1003.4600.

J.-P., Kahane [2013] Sur un ensemble de Besicovitch, Enseign. Math. 59, 307–324.Google Scholar

J.-P., Kahane and R., Salem [1963] Ensembles parfaits et séries trigonométriques, Hermann.

S., Kakeya [1917] Some problems on maxima and minima regarding ovals, Tohoku Science Reports 6, 71–88.Google Scholar

N. H., Katz [1996] A counterexample for maximal operators over a Cantor set of directions, Math. Res. Lett. 3, 527-536.Google Scholar

N. H., Katz [1999] Remarks on maximal operators over arbitrary sets of directions, Bull. London Math. Soc. 31, 700–710.Google Scholar

N. H., Katz, I., Łaba and T., Tao [2000] An improved bound on the Minkowski dimension of Besicovitch sets in ℝ3, Ann. of Math. (2) 152, 383–446.Google Scholar

N. H., Katz and T., Tao [1999] Bounds on arithmetic projections, and applications to the Kakeya conjecture, Math. Res. Lett. 6, 625–630.Google Scholar

N. H., Katz and T., Tao [2001] Some connections between Falconer's distance set conjecture and sets of Furstenburg type, New York J. Math. 7, 149–187.Google Scholar

N. H., Katz and T., Tao [2002a] New bounds for Kakeya problems, J. Anal. Math. 87, 231–263.Google Scholar

N. H., Katz and T., Tao [2002b] Recent progress on the Kakeya conjecture, Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, 2000, Publ. Mat., 161–179.Google Scholar

Y., Katznelson [1968] An Introduction to Harmonic Analysis, Dover Publications.

R., Kaufman [1968] On Hausdorff dimension of projections, Mathematika 15, 153–155.Google Scholar

R., Kaufman [1969] An exceptional set for Hausdorff dimension, Mathematika 16, 57–58.

R., Kaufman [1973] Planar Fourier transforms and Diophantine approximation, Proc. Amer.Math. Soc. 40, 199–204.Google Scholar

R., Kaufman [1975] Fourier analysis and paths of Brownian motion, Bull. Soc. Math. France 103, 427–432.Google Scholar

R., Kaufman [1981] On the theorem of Jarnik and Besicovitch, Acta Arith. 39, 265–267.Google Scholar

R., Kaufman and P., Mattila [1975] Hausdorff dimension and exceptional sets of linear transformations, Ann. Acad. Sci. Fenn. Ser. A I Math. 1, 387–392.Google Scholar

A. S., Kechris and A., Louveau [1987] Descriptive Set Theory and the Structure of Sets of Uniqueness, London Math. Soc. Lecture Notes 128, Cambridge University Press.

U., Keich [1999] On Lp bounds for Kakeya maximal functions and the Minkowski dimension in ℝ2, Bull. London Math. Soc. 31, 213–221.Google Scholar

T., Keleti [1998] A 1-dimensional subset of the reals that intersects each of its translates in at most a single point, Real Anal. Exchange 24, 843–844.Google Scholar

T., Keleti [2008] Construction of one-dimensional subsets of the reals not containing similar copies of given patterns, Anal. PDE, 1, 29–33.Google Scholar

T., Keleti [2014] Are lines bigger than line segments?, arXiv:1409.5992.

T., Kempton [2013] Sets of beta-expansions and the Hausdorff measure of slices through fractals, to appear in J. Eur. Math. Soc., arXiv:1307.2091.

C. E., Kenig and T., Toro [2003] Poisson kernel characterization of Reifenberg flat chord arc domains, Ann. Sci. École Norm. Sup. 36, 323–401.Google Scholar

R., Kenyon [1997] Projecting the one-dimensional Sierpinski gasket, Israel J. Math. 97, 221–238.Google Scholar

R., Kenyon and Y., Peres [1991] Intersecting random translates of invariant Cantor sets, Invent. Math. 104, 601–629.Google Scholar

J., Kim [2009] Two versions of the Nikodym maximal function on the Heisenberg group, J. Funct. Anal. 257, 1493−1518.Google Scholar

J., Kim [2012] Nikodym maximal functions associated with variable planes in ℝ3, Integral Equations Operator Theory 73, 455–480.Google Scholar

L., Kolasa and T. W., Wolff [1999] On some variants of the Kakeya problem, Pacific J. Math. 190, 111–154.Google Scholar

S., Konyagin and I., Łaba [2006] Distance sets of well-distributed planar sets for polygonal norms, Israel J. Math. 152, 157–179.Google Scholar

T., Körner [2003] Besicovitch via Baire, Studia Math. 158, 65–78.Google Scholar

T., Körner [2009] Fourier transforms of measures and algebraic relations on their supports, Ann. Inst. Fourier (Grenoble) 59, 1291–1319.Google Scholar

T., Körner [2011] Hausdorff and Fourier dimension, Studia Math. 206, 37–50.Google Scholar

T., Körner [2014] Fourier transforms of distributions and Hausdorff measures, J. Fourier Anal. Appl. 20, 547–556.Google Scholar

G., Kozma and A., Olevskii [2013] Singular distributions, dimension of support, and symmetry of Fourier transform, Ann. Inst. Fourier (Grenoble) 63, 1205–1226.Google Scholar

E., Kroc and M., Pramanik [2014a] Kakeya-type sets over Cantor sets of directions in ℝd+1, arXiv:1404.6235.

G., Kozma and A., Olevskii [2014b] Lacunarity, Kakeya-type sets and directional maximal operators, arXiv:1404.6241.

I., Łaba [2008] From harmonic analysis to arithmetic combinatorics, Bull. Amer. Math. Soc. (N.S.) 45, 77–115.Google Scholar

I., Łaba [2012] Recent progress on Favard length estimates for planar Cantor sets, arXiv:1212.0247.

I., Łaba [2014] Harmonic analysis and the geometry of fractals, Proceedings of the 2014 International Congress of Mathematicians.

I., Łaba and M., Pramanik [2009] Arithmetic progressions in sets of fractional dimension, Geom. Funct. Anal. 19, 429–456.Google Scholar

I., Łaba and T., Tao [2001a] An improved bound for the Minkowski dimension of Besicovitch sets in medium dimension, Geom. Funct. Anal. 11, 773–806.Google Scholar

I., Łaba and T., Tao [2001b] An X-ray transform estimate in ℝn, Rev. Mat. Iberoam. 17, 375–407.Google Scholar

I., Łaba and T. W., Wolff [2002] A local smoothing estimate in higher dimensions, J. Anal. Math. 88, 149–171.Google Scholar

I., Łaba and K., Zhai [2010] The Favard length of product Cantor sets, Bull. London Math. Soc. 42, 997–1009.Google Scholar

J., Lagarias and Y., Wang [1996] Tiling the line with translates of one tile, Invent. Math. 124, 341–365.Google Scholar

N. S., Landkof [1972] Foundations of Modern Potential Theory, Springer-Verlag.

F., Ledrappier and E., Lindenstrauss [2003] On the projections of measures invariant under the geodesic flow, Int. Math. Res. Not. 9, 511–526.Google Scholar

S., Lee [2004] Improved bounds for Bochner–Riesz and maximal Bochner–Riesz operators, Duke Math. J. 122, 205–232.Google Scholar

S., Lee [2006a] Bilinear restriction estimates for surfaces with curvatures of different signs, Trans. Amer. Math. Soc. 358, 3511–3533.Google Scholar

S., Lee [2006b] On pointwise convergence of the solutions to Schrödinger equations in ℝ2, Int. Math. Res. Not., Art. ID 32597, 21 pp.Google Scholar

S., Lee, K. M., Rogers and A., Seeger [2013] On space-time estimates for the Schrödinger operator, J. Math. Pures Appl.(9) 99, 62–85.Google Scholar

S., Lee and A., Vargas [2010] Restriction estimates for some surfaces with vanishing curvatures, J. Funct. Anal. 258, 2884–2909.Google Scholar

Y., Lima and C. G., Moreira [2011] Yet another proof of Marstrand's theorem, Bull. Braz. Math. Soc. (N.S.) 42, 331–345.Google Scholar

E., Lindenstrauss and N., de Saxcé [2014] Hausdorff dimension and subgroups of SU(2), to appear in Israel J. Math.

B., Liu [2014] On radii of spheres determined by subsets of Euclidean space, J. Fourier Anal. Appl. 20, 668–678.Google Scholar

Q. H., Liu, L., Xi and Y. F., Zhao [2007] Dimensions of intersections of the Sierpinski carpet with lines of rational slopes, Proc. Edinb. Math. Soc. (2) 50, 411–427.Google Scholar

R., Lucà and K. M., Rogers [2015] Average decay of the Fourier transform of measures with applications, arXiv:1503.00105.

R., Lyons [1995] Seventy years of Rajchman measures, J. Fourier Anal. Appl., 363–377, Kahane Special Issue.Google Scholar

P., Maga [2010] Full dimensional sets without given patterns, Real Anal. Exchange 36 (2010/11), 79–90.Google Scholar

A., Manning and K., Simon [2013] Dimension of slices through the Sierpinski carpet, Trans. Amer. Math. Soc. 365, 213–250.Google Scholar

J. M., Marstrand [1954] Some fundamental geometrical properties of plane sets of fractional dimensions, Proc. London Math. Soc. (3) 4, 257–302.Google Scholar

J. M., Marstrand [1979] Packing planes in ℝ3, Mathematika 26, 180–183.Google Scholar

J. M., Marstrand [1987] Packing circles in the plane, Proc. London Math. Soc. 55, 37–58.Google Scholar

P., Mattila [1975] Hausdorff dimension, orthogonal projections and intersections with planes, Ann. Acad. Sci. Fenn. Ser. A I Math. 1, 227–244.Google Scholar

P., Mattila [1981] Integralgeometric properties of capacities, Trans. Amer. Math. Soc. 266, 539–554.Google Scholar

P., Mattila [1984] Hausdorff dimension and capacities of intersections of sets in n-space, Acta Math. 152, 77–105.Google Scholar

P., Mattila [1985] On the Hausdorff dimension and capacities of intersections, Mathematika 32, 213–217.Google Scholar

P., Mattila [1987] Spherical averages of Fourier transforms of measures with finite energy; dimension of intersections and distance sets, Mathematika 34, 207–228.Google Scholar

P., Mattila [1990] Orthogonal projections, Riesz capacities, and Minkowski content, Indiana Univ. Math. J. 39, 185–198.Google Scholar

P., Mattila [1995] Geometry of Sets and Measures in Euclidean Spaces, Cambridge University Press.

P., Mattila [2004] Hausdorff dimension, projections, and the Fourier transform, Publ. Mat. 48, 3–48.Google Scholar

P., Mattila [2014] Recent progress on dimensions of projections, in Geometry and Analysis of Fractals, D.-J., Feng and K.-S., Lau (eds.), Springer Proceedings in Mathematics and Statistics 88, Springer-Verlag, 283–301.

P., Mattila and P., Sjölin [1999] Regularity of distance measures and sets, Math. Nachr. 204, 157–162.Google Scholar

W., Minicozzi and C., Sogge [1997] Negative results for Nikodym maximal functions and related oscillatory integrals in curved space, Math. Res. Lett. 4, 221– 237.Google Scholar

T., Mitsis [1999] On a problem related to sphere and circle packing, J. London Math.Soc. (2) 60, 501–516.Google Scholar

T., Mitsis [2002a] A note on the distance set problem in the plane, Proc. Amer. Math. Soc. 130, 1669–1672.Google Scholar

T., Mitsis [2002b] A Stein-Tomas restriction theorem for general measures, Publ. Math. Debrecen 60, 89–99.Google Scholar

T., Mitsis [2003a] Topics in Harmonic Analysis, University of Jyväskylä, Department of Mathematics and Statistics, Report 88.Google Scholar

T., Mitsis [2003b] An optimal extension of Marstrand's plane-packing theorem, Arch. Math. 81, 229–232.Google Scholar

T., Mitsis [2004a] (n, 2)-sets have full Hausdorff dimension, Rev. Mat. Iberoam. 20, 381–393, Corrigenda: Rev. Mat. Iberoam. 21 (2005), 689–692.Google Scholar

T., Mitsis [2004b] On Nikodym-type sets in high dimensions, Studia Math. 163, 189–192.Google Scholar

T., Mitsis [2005] Norm estimates for a Kakeya-typemaximal operator, Math. Nachr. 278, 1054–1060.Google Scholar

G., Mockenhaupt [2000] Salem sets and restriction properties of Fourier transforms, Geom. Funct. Anal. 10, 1579–1587.Google Scholar

U., Molter, and E., Rela [2010] Improving dimension estimates for Furstenberg-type sets, Adv. Math. 223, 672–688.Google Scholar

U., Molter, and E., Rela [2012] Furstenberg sets for a fractal set of directions, Proc. Amer. Math. Soc. 140, 2753–2765.Google Scholar

U., Molter, and E., Rela [2013] Small Furstenberg sets, J. Math. Anal. Appl. 400, 475–486.Google Scholar

C. G., Moreira [1998] Sums of regular Cantor sets, dynamics and applications to number theory, Period. Math. Hungar. 37, 55–63.Google Scholar

C. G., Moreira and J.–C., Yoccoz [2001] Stable intersections of regular Cantor sets with large Hausdorff dimensions, Ann. of Math. (2) 154, 45–96.Google Scholar

P., Mörters and Y., Peres [2010] Brownian Motion, Cambridge University Press.

D., Müller [2012] Problems of Harmonic Analysis related to finite type hypersurfaces in ℝ3, and Newton polyhedra, arXiv:1208.6411.

C., Muscalu and W., Schlag [2013] Classical and Multilinear Harmonic Analysis I, Cambridge University Press.

F., Nazarov, Y., Peres and P., Shmerkin [2012] Convolutions of Cantor measures without resonance, Israel J. Math. 187, 93–116.Google Scholar

F., Nazarov, Y., Peres and A., Volberg [2010] The power law for the Buffon needle probability of the four-corner Cantor set, Algebra i Analiz 22, 82–97; translation in St. Petersburg Math. J. 22 (2011), 61–72.Google Scholar

F., Nazarov, X., Tolsa and A., Volberg [2014] On the uniform rectifiability of AD regular measures with bounded Riesz transform operator: the case of codimension 1, Acta Math. 213, 237–321.Google Scholar

E. M., Nikishin [1972] A resonance theorem and series in eigenfunctions of the Laplace operator, Izv. Akad. Nauk SSSR Ser. Mat. 36, 795–813 (Russian).Google Scholar

O., Nikodym [1927] Sur la measure des ensembles plans dont tous les points sont rectilinearément accessibles, Fund. Math. 10, 116–168.Google Scholar

D. M., Oberlin [2006a] Restricted Radon transforms and unions of hyperplanes, Rev. Mat. Iberoam. 22, 977–992.Google Scholar

D. M., Oberlin [2006b] Packing spheres and fractal Strichartz estimates in ℝd for d ≥ 3, Proc. Amer. Math. Soc. 134, 3201–3209.Google Scholar

D. M., Oberlin [2007] Unions of hyperplanes, unions of spheres, and some related estimates, Illinois J. Math. 51, 1265–1274.Google Scholar

D. M., Oberlin [2012] Restricted Radon transforms and projections of planar sets, Canad. Math. Bull. 55, 815–820.Google Scholar

D. M., Oberlin [2014a] Exceptional sets of projections, unions of k-planes, and associated transforms, Israel J. Math. 202, 331–342.Google Scholar

D. M., Oberlin [2014b] Some toy Furstenberg sets and projections of the four-corner Cantor set, Proc. Amer. Math. Soc. 142, 1209–1215.Google Scholar

D. M., Oberlin and R., Oberlin [2013a] Unit distance problems, arXiv:1307.5039.

D. M., Oberlin and R., Oberlin [2013b] Application of a Fourier restriction theorem to certain families of projections in ℝ3, arXiv:1307.5039.

D. M., Oberlin and R., Oberlin [2014] Spherical means and pinned distance sets, arXiv:1411.0915.

R., Oberlin [2007] Bounds for Kakeya-type maximal operators associated with k-planes, Math. Res. Lett. 14, 87–97.Google Scholar

R., Oberlin [2010] Two bounds for the X-ray transform, Math. Z. 266, 623–644.Google Scholar

T., Orponen [2012a] On the distance sets of self-similar sets, Nonlinearity 25, 1919–1929.Google Scholar

T., Orponen [2012b] On the packing dimension and category of exceptional sets of orthogonal projections, to appear in Ann. Mat. Pur. Appl., arXiv:1204.2121.

T., Orponen [2014a] Slicing sets and measures, and the dimension of exceptional parameters, J. Geom. Anal. 24, 47–80.Google Scholar

T., Orponen [2014b] Non-existence of multi-line Besicovitch sets, Publ. Mat. 58, 213–220.Google Scholar

T., Orponen [2013a] Hausdorff dimension estimates for some restricted families of projections in ℝ3, arXiv:1304.4955.

T., Orponen [2013b] On the packing measure of slices of self-similar sets, arXiv:1309.3896.

T., Orponen [2013c] On the tube-occupancy of sets in ℝd, to appear in Int. Math. Res. Not., arXiv:1311.7340.

T., Orponen [2014c] A discretised projection theorem in the plane, arXiv:1407.6543.

T., Orponen and T., Sahlsten [2012] Tangent measures of non-doubling measures, Math. Proc. Cambridge Philos. Soc. 152, 555–569.Google Scholar

W., Ott, B., Hunt and V., Kaloshin [2006] The effect of projections on fractal sets and measures in Banach spaces, Ergodic Theory Dynam. Systems 26, 869–891.Google Scholar

J., Parcet and K. M., Rogers [2013] Differentiation of integrals in higher dimensions, Proc. Natl. Acad. Sci. USA 110, 4941–4944.Google Scholar

A., Peltomäki [1987] Licentiate thesis (in Finnish), University of Helsinki.

Y., Peres and M., Rams [2014] Projections of the natural measure for percolation fractals, arXiv:1406.3736.

Y., Peres and W., Schlag [2000] Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions, Duke Math. J. 102, 193–251.Google Scholar

Y., Peres, W., Schlag and B., Solomyak [2000] Sixty years of Bernoulli convolutions, in Fractal Geometry and Stochastics II, Birkhäuser, 39–65.

Y., Peres and P., Shmerkin [2009] Resonance between Cantor sets, Ergodic Theory Dynam. Systems 29, 201–221.Google Scholar

Y., Peres, K., Simon and B., Solomyak [2000] Self-similar sets of zero Hausdorff measure and positive packing measure, Israel J. Math. 117, 353–379.Google Scholar

Y., Peres, K., Simon and B., Solomyak [2003] Fractals with positive length and zero buffon needle probability, Amer. Math. Monthly 110, 314–325.Google Scholar

Y., Peres and B., Solomyak [1996] Absolute continuity of Bernoulli convolutions, a simple proof, Math. Res. Lett. 3, 231–239.Google Scholar

Y., Peres and B., Solomyak [1998] Self-similar measures and intersections of Cantor sets, Trans. Amer. Math. Soc. 350, 4065–4087.Google Scholar

Y., Peres and B., Solomyak [2002] How likely is Buffon's needle to fall near a planar Cantor set?, Pacific J. Math. 204, 473–496.Google Scholar

J., Peyriére [1975] Étude de quelques propriétés des produits de Riesz, Ann. Inst. Fourier Grenoble 25, 127–169.Google Scholar

G., Pisier [1986] Factorization of operators through Lp∞ or Lp and noncommutative generalizations, Math. Ann. 276, 105–136.Google Scholar

M., Pollicott and K., Simon [1995] TheHausdorff dimension of λ-expansions with deleted digits, Trans. Amer. Math. Soc. 347, 967–983.Google Scholar

A., Poltoratski [2012] Spectral gaps for sets and measures, Acta Math. 208, 151–209.Google Scholar

D., Preiss [1987] Geometry of sets and measures in ℝn; distribution, rectifiability, and densities, Ann. of Math. (2) 125, 537–643.Google Scholar

M., Rams and K., Simon [2014] The dimension of projections of fractal percolations, J. Stat. Phys. 154, 633–655.Google Scholar

M., Rams and K., Simon [2015] Projections of fractal percolations, Ergodic Theory Dyn. Systems 35, 530–545.Google Scholar

F., Riesz [1918] Über die Fourierkoeffizienten einer stetigen Funktion von Beschränkter Schwankung, Math. Z. 2, 312–315.Google Scholar

K. M., Rogers [2006] On a planar variant of the Kakeya problem, Math. Res. Lett. 13, 199–213.Google Scholar

V. A., Rokhlin [1962] On the fundamental ideas of measure theory, Trans. Amer.Math. Soc., Series 1, 10, 1–52.Google Scholar

K., Roth [1953] On certain sets of integers, J. London. Math. Soc. 28, 104–109.Google Scholar

R., Salem [1944] A remarkable class of algebraic integers. Proof of a conjecture by Vijayaraghavan, Duke Math. J. 11, 103–108.Google Scholar

R., Salem [1951] On singular monotonic functions whose spectrum has a given Hausdorff dimension, Ark. Mat. 1, 353–365.Google Scholar

R., Salem [1963] Algebraic Numbers and Fourier Analysis, Heath Mathematical Monographs.

E., Sawyer [1987] Families of plane curves having translates in a set of measure zero, Mathematika 34, 69–76.Google Scholar

N. de, Saxcé [2013] Subgroups of fractional dimension in nilpotent or solvable Lie groups, Mathematika 59, 497–511.Google Scholar

N. de, Saxcé [2014] Borelian subgroups of simple Lie groups, arXiv:1408.1579.

W., Schlag [1998] A geometric inequality with applications to the Kakeya problem in three dimensions, Duke Math. J. 93, 505–533.Google Scholar

B., Shayya [2011] Measures with Fourier transforms in L2 of a half-space, Canad. Math. Bull. 54, 172–179.Google Scholar

B., Shayya [2012] When the cone in Bochner's theorem has an opening less than π, Bull. London Math. Soc. 44, 207–221.Google Scholar

N.-R., Shieh and Y., Xiao [2006] Images of Gaussian random fields: Salem sets and interior points, Studia Math. 176, 37–60.Google Scholar

N.-R., Shieh and X., Zhang [2009] Random p-adic Riesz products: Continuity, singularity, and dimension, Proc. Amer. Math. Soc. 137, 3477–3486.Google Scholar

P., Shmerkin [2014] On the exceptional set for absolute continuity of Bernoulli convolutions, Geom. Funct. Anal. 24, 946–958.Google Scholar

P., Shmerkin and B., Solomyak [2014] Absolute continuity of self-similar measures, their projections and convolutions, arXiv:1406.0204.

P., Shmerkin and V., Suomala [2012] Sets which are not tube null and intersection properties of random measures, to appear in J. London Math. Soc., arXiv:1204.5883.

P., Shmerkin and V., Suomala [2014] Spatially independent martingales, intersections, and applications, arXiv:1409.6707.

K., Simon and L., Vágó [2014] Projections of Mandelbrot percolation in higher dimensions, arXiv:1407.2225.

P., Sjölin [1993] Estimates of spherical averages of Fourier transforms and dimensions of sets, Mathematika 40, 322–330.Google Scholar

P., Sjölin [1997] Estimates of averages of Fourier transforms of measures with finite energy, Ann. Acad. Sci. Fenn. Ser. A I Math. 22, 227–236.Google Scholar

P., Sjölin [2002] Spherical harmonics and spherical averages of Fourier transforms, Rend. Sem. Mat. Univ. Padova 108, 41–51.Google Scholar

P., Sjölin [2007] Maximal estimates for solutions to the nonelliptic Schrödinger equation, Bull. London Math. Soc. 39, 404–412.Google Scholar

P., Sjölin [2013] Nonlocalization of operators of Schrödinger type, Ann. Acad. Sci. Fenn. Ser. A I Math. 38, 141–147.Google Scholar

P., Sjölin and F., Soria [2003] Estimates of averages of Fourier transforms with respect to general measures, Proc. Royal Soc. Edinburgh A 133, 943–950.Google Scholar

P., Sjölin and F., Soria [2014] Estimates for multiparameter maximal operators of Schrödinger type, J. Math. Anal. Appl. 411, 129–143.Google Scholar

C. D., Sogge [1991] Propagation of singularities and maximal functions in the plane, Invent. Math. 104, 349–376.Google Scholar

C. D., Sogge [1993] Fourier Integrals in Classical Analysis, Cambridge University Press.

C. D., Sogge [1999] Concerning Nikodym-type sets in 3-dimensional curved spaces, J. Amer.Math. Soc. 12, 1–31.Google Scholar

B., Solomyak [1995] On the random series Σ±λn (an Erdȍs problem), Ann. of Math. (2) 142, 611–625.Google Scholar

E. M., Stein [1961] On limits of sequences of operators, Ann. of Math. (2) 74, 140–170.Google Scholar

E. M., Stein [1986] Oscillatory integrals in Fourier analysis, Beijing Lectures in Harmonic Analysis, pp. 307–355, Annals of Math. Studies 112, Princeton University Press.

E. M., Stein [1993] Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory integrals, Princeton University Press.

E. M., Stein and G., Weiss [1971] Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press.

R., Strichartz [1977] Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44, 705–714.Google Scholar

R., Strichartz [1989] Besicovitch meets Wiener–Fourier expansions and fractal measures, Bull. Amer. Math. Soc. (N.S.) 20, 55–59.Google Scholar

R., Strichartz [1990a] Fourier asymptotics of fractal measures, J. Funct. Anal. 89, 154–187.Google Scholar

R., Strichartz [1990b] Self-similar measures and their Fourier transforms I, Indiana Univ. Math. J. 39, 797–817.Google Scholar

R., Strichartz [1993a] Self-similar measures and their Fourier transforms II, Trans. Amer. Math. Soc. 336, 335–361.Google Scholar

R., Strichartz [1993b] Self-similar measures and their Fourier transforms III, Indiana Univ. Math. J. 42, 367–411.Google Scholar

R., Strichartz [1994] A Guide to Distribution Theory and Fourier Transforms, Studies in Advanced Mathematics, CRC Press.

T., Tao [1999a] Bochner–Riesz conjecture implies the restriction conjecture, DukeMath. J. 96, 363–375.Google Scholar

T., Tao [1999b] Lecture notes for the course Math 254B, Spring 1999 at UCLA, www.math.ucla.edu/tao/254b.1.99s/

T., Tao [2000] Finite field analogues of the Erdos, Falconer, and Furstenburg problems, www.math.ucla.edu/tao/preprints/kakeya.html.

T., Tao [2001] From rotating needles to stability of waves: emerging connections between combinatorics, analysis, and PDE, Notices Amer. Math. Soc. 48, 294–303.Google Scholar

T., Tao [2003] A sharp bilinear restriction estimate for paraboloids, Geom. Funct. Anal. 13, 1359–1384.Google Scholar

T., Tao [2004] Some recent progress on the restriction conjecture in Fourier analysis and convexity, 217–243, Appl. Numer. Harmon. Anal., Birkhäuser Boston, Boston, MA.

T., Tao [2008a] Dvir's proof of the finite field Kakeya conjecture, http://terrytao.wordpress.com/2008/03/24/dvirs-proof-of-the-finite-field-kakeya-conjecture, 24 March 2008.

T., Tao [2008b] A remark on the Kakeya needle problem, http://terrytao.wordpress.com/2008/12/31/a-remark-on-the-kakeya-needle-problem.

T., Tao [2009] A quantitative version of the Besicovitch projection theorem via multiscale analysis, Proc. London Math. Soc. 98, 559–584.Google Scholar

T., Tao [2011] An epsilon of room, II: pages from year three of a mathematical blog, Amer. Math. Soc.

T., Tao [2014] Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory, EMS Surv. Math. Sci. 1, 1–46.Google Scholar

T.|Tao and A., Vargas [2000] A bilinear approach to cone multipliers I. Restriction estimates, Geom. Funct. Anal. 10, 185–215.Google Scholar

T., Tao, A., Vargas and L., Vega [1998] A bilinear approach to the restriction and Kakeya conjectures, J. Amer.Math. Soc. 11, 967–1000.Google Scholar

T., Tao and V., Vu [2006] Additive Combinatorics, Cambridge University Press.

F., Temur [2014] A Fourier restriction estimate for surfaces of positive curvature in ℝ6, Rev. Mat. Iberoam. 30, 1015–1036.Google Scholar

X., Tolsa [2014] Analytic capacity, the Cauchy Transform, and Non-homogeneous Calderón-Zygmund Theory, Birkhäuser.

P. A., Tomas [1975] A restriction theorem for the Fourier transform, Bull. Amer. Math Soc. 81, 477–478.Google Scholar

G., Travaglini [2014] Number Theory, Fourier Analysis and Geometric Discrepancy, London Mathematical Society Student Texts 81, Cambridge University Press.

A., Vargas [1991] Operadores maximales, multiplicadores de Bochner–Riesz y teoremas de restricción, Master's thesis, Universidad Autónoma de Madrid.

A., Volberg and V., Eiderman [2013] Nonhomogeneous harmonic analysis: 16 years of development, Uspekhi Mat. Nauk. 68, 3–58; translation in Russian Math. Surveys 68, 973–1026.Google Scholar

N. G., Watson [1944] A Treatise on Bessel Functions, Cambridge University Press.

Z.-Y., Wen, W., Wu and L., Xi [2013] Dimension of slices through a self-similar set with initial cubical pattern, Ann. Acad. Sci. Fenn. Ser. A I Math. 38, 473–487.Google Scholar

Z.-Y., Wen and L., Xi [2010] On the dimension of sections for the graph-directed sets, Ann. Acad. Sci. Fenn. Ser. A I Math. 35, 515–535.Google Scholar

L., Wisewell [2004] Families of surfaces lying in a null set, Mathematika 51, 155–162.Google Scholar

L., Wisewell [2005] Kakeya sets of curves, Geom. Funct. Anal. 15, 1319–1362.Google Scholar

T. W., Wolff [1995] An improved bound for Kakeya type maximal functions, Rev. Mat. Iberoam. 11, 651–674.Google Scholar

T. W., Wolff [1997] A Kakeya-type problem for circles, Amer. J. Math. 119, 985–1026.Google Scholar

T. W., Wolff [1998] A mixed norm estimate for the X-ray transform, Rev. Mat. Iberoam. 14, 561–600.Google Scholar

T. W., Wolff [1999] Decay of circular means of Fourier transforms of measures, Int. Math. Res. Not. 10, 547–567.Google Scholar

T. W., Wolff [2000] Local smoothing type estimates on Lp for large p, Geom. Funct. Anal. 10, 1237–1288.Google Scholar

T. W., Wolff [2001] A sharp bilinear cone restriction estimate, Ann. of Math. (2) 153, 661–698.Google Scholar

T. W., Wolff [2003] Lectures on Harmonic Analysis, Amer. Math. Soc., University Lecture Series 29.Google Scholar

Y., Xiao [2013] Recent developments on fractal properties of Gaussian random fields, in Further Developments in Fractals and Related Fields, J. Barral and S. Seuret (eds.), Trends in Mathematics, Birkhäuser, 255–288.

Y., Xiong and J., Zhou [2005] The Hausdorff measure of a class of Sierpinski carpets, J. Math. Anal. Appl. 305, 121–129.Google Scholar

W. P., Ziemer [1989] Weakly Differentiable Functions, Springer-Verlag.

A., Zygmund [1959] Trigonometric Series, volumes I and II, Cambridge University Press (the first edition 1935 in Warsaw).

W. P., Ziemer [1974] On Fourier coefficients and transforms of functions of two variables, Studia Math. 50, 189–201.Google Scholar

Book contents

References

Summary

Access options

References

Book contents

References

Summary

Access options

References

Save book to Kindle

Save book to Dropbox

Save book to Google Drive