Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-28T06:47:28.611Z Has data issue: false hasContentIssue false

On rearranging maximal functions in Rn

Published online by Cambridge University Press:  20 January 2009

P. L. Walker
Affiliation:
University of Lancaster
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
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), 1013.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), 139143.CrossRefGoogle Scholar