Lp→Lq bounds for spherical maximal operators

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

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.

Citation

Anderson, T., Hughes, K., Roos, J., & Seeger, A. (2021). Lp→Lq bounds for spherical maximal operators. Mathematische Zeitschrift, 297(3-4), 1057-1074. https://doi.org/10.1007/s00209-020-02546-0

• 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