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A note on a paper of E.R. Love

Published online by Cambridge University Press:  17 April 2009

F. Fehér
F. Fehér
Affiliation:
Lehrstuhl A für Mathematik, Rheinisch-Westfäl ische Technische Hochschule Aachen, Aachen, Germany.
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Abstract

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Applying a new and very elegant method of proof of the Schur-Hardy inequality, given by E.R. Love at the Oberwolfach conference on Linear Spaces and Approximation (1977), norm estimates of integral operators with homogeneous kernels are established in the setting of abstract function norms. Applications to Flett's inequality, to integral means, and to fractional integrals are given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 1 , August 1978 , pp. 67 - 75
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Aranda, Pedro Jorge et Cattáneo, Enrique Paule, “Sur les espaces de Lorentz avec poids”, C.R. Acad. Sci. Paris Ser. A 264 (1967), 109–112.Google Scholar
[2]Boyd, David W., “Indices of function spaces and their relationship to interpolation”, Canad. J. Math. 21 (1969), 1245–1254.CrossRefGoogle Scholar
[3]Butzer, P.L. and Fehér, F., “Generalized Hardy and Hardy-Littlewood inequalities in rearrangement-invariant spaces”, Comment. Math. Prace Mat. (to appear).Google Scholar
[4]Cotlar, Mischa and Cignoli, Roberto, An introduction to functional analysis (translated by Torchinsky, A. and Villalobos, A. González. North-Holland, Amsterdam, London; American Elsevier, New York, 1974).Google Scholar
[5]Fehér, F., “Interpolation und Indexbedingungen auf rearrangement-invarianten Funktionenraumen. I. Grundlagen und die X-Methode”, J. Functional Analysis 25 (1977), 147–161.Google Scholar
[6]Flett, T.M., “A note on some inequalities”, Proc. Glasgow Math. Assoc. 4 (1959–1960), 7–15.Google Scholar
[7]Hardy, G.H., Littlewood, J.E., Pólya, G., Inequalities, 2nd edition (Cambridge University Press, Cambridge, 1952; reprinted 1959).Google Scholar
[8]Love, Eric Russell, “Some inequalities for fractional integrals”, Linear spaces and approximation (Proc. Conf. Mathematical Research Institute, Oberwolfach, 1977, 177–184. International Series of Numerical Mathematics, 40. Birkhäuser Verlag, Basel, Stuttgart, 1978).Google Scholar
[9]Luxemburg, W.A.J. and Zaanen, A.C., Riesz spaces, volume I (North-Holland, Amsterdam, London, 1971).Google Scholar
[10]Rooney, P.G., “A generalization of some theorems of Hardy”, Trans. Roy. Soc. Canada Sect. III (3) 49 (1955), 59–66.Google Scholar
[11]Rooney, P.G., “On some properties of certain fractional integrals”, Trans. Roy. Soc. Canada Sect. III (3) 50 (1956), 61–70.Google Scholar
[12]Strichartz, Robert S., “LP estimates for integral transforms”, Trans. Amer. Math. Soc. 136 (1969), 33–50.Google Scholar
[13]Walsh, T., “On LP estimates for integral transforms”, Trans. Amer. Math. Soc. 155 (1971), 195–215.Google Scholar