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Lp→Lq bounds for spherical maximal operators

Anderson, T.; Hughes, K.; Roos, J.; Seeger, A.

Authors

T. Anderson

K. Hughes

J. Roos

A. Seeger



Abstract

Let f∈Lp(Rd), d≥3, and let Atf(x) be the average of f over the sphere with radius t centered at x. For a subset E of [1, 2] we prove close to sharp Lp→Lq estimates for the maximal function supt∈E|Atf|. A new feature is the dependence of the results on both the upper Minkowski dimension of E and the Assouad dimension of E. The result can be applied to prove sparse domination bounds for a related global spherical maximal function.

Journal Article Type Article
Acceptance Date Mar 9, 2020
Online Publication Date Jun 5, 2020
Publication Date 2021-04
Deposit Date Nov 21, 2022
Journal Mathematische Zeitschrift
Print ISSN 0025-5874
Electronic ISSN 1432-1823
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 297
Issue 3-4
Pages 1057-1074
DOI https://doi.org/10.1007/s00209-020-02546-0
Keywords Lp -improving estimates, Spherical maximal functions, Minkowski dimension, Assouad dimension, Assouad spectrum, Sparse domination
Public URL http://researchrepository.napier.ac.uk/Output/2963145