Lp→Lq bounds for spherical maximal operators

Theresa C. Anderson, Kevin Hughes, Joris Roos, Andreas Seeger

Research output: Contribution to journalArticlepeer-review

Abstract

Let f∈Lp(Rd), d≥3, and let Atf(x) 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.
Original languageEnglish
Number of pages20
JournalMathematische zeitschrift
Early online date5 Jun 2020
DOIs
Publication statusE-pub ahead of print - 5 Jun 2020

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