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On rearranging maximal functions in Rn

Published online by Cambridge University Press:  20 January 2009

P. L. Walker
P. L. Walker
Affiliation:
University of Lancaster
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Denote by f a positive measurable function on Rn, and by λ the distribution function of denotes the Lebesgue measure of the set specified. We shall suppose that λ(y)<∞ for each y>0, and that λ(y)→0 as y→∞. The decreasing rearrangement f* of f is defined on (0, ∞) by

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 4 , September 1975 , pp. 363 - 369
Copyright
Copyright © Edinburgh Mathematical Society 1975

References

REFERENCES

(1) Guzmán, M. de and Welland, G. V., On the differentiation of integrals, Rev. Un. Math. Argentina, 25 (1971).Google Scholar
(2) Herz, C. S., The Hardy-Littlewood Maximal Theorem, Symposium in Harmonic Analysis (University of Warwick, 1968).Google Scholar
(3) Riesz, F., Sur un théorèm de maximum de MM Hardy et Littlewood, J. London Math. Soc. 7 (1931), 10–13.Google Scholar
(4) Stein, E. M., Singular integrals and differentiability properties of functions (Princeton, 1970).Google Scholar
(5) Stein, E. M. and Weiss, G., Introduction to harmonic analysis on Euclidean spaces (Princeton, 1971).Google Scholar
(6) Walker, P. L., Some estimates for the Hardy-Littlewood maximal function in Rn, Bull. London Math. Soc. 7 (1975), 139–143.CrossRefGoogle Scholar