$L^p$ bound on the strong spherical maximal function

TL;DR

This paper establishes the boundedness of the strong spherical maximal function on L^p spaces for certain p values in dimensions three and higher, advancing understanding of maximal functions in harmonic analysis.

Contribution

It proves new L^p bounds for the strong spherical maximal function in dimensions d ≥ 3, extending previous results in harmonic analysis.

Findings

Boundedness of the strong spherical maximal function for p > 2(d+1)/(d-1)

Applicable in dimensions d ≥ 3

Advances theoretical understanding of maximal functions

Abstract

In this note we show that the strong spherical maximal function in $\mathbb R^d$ is bounded on $L^p$ if $p>2(d+1)/(d-1)$ for $d\ge 3$.