Lebesgue space estimates for spherical maximal functions on Heisenberg groups

TL;DR

This paper establishes sharp Lebesgue space bounds for spherical maximal functions on Heisenberg groups, improving sparse domination bounds and extending results to lacunary variants and Me9tivier groups.

Contribution

It provides the first sharp $L^p o L^q$ estimates for local spherical maximal operators on Heisenberg groups, including extensions to lacunary and Me9tivier groups.

Findings

Sharp $L^p o L^q$ estimates for spherical maximal functions.

Improved bounds on sparse domination for global maximal operators.

Extensions to lacunary variants and Me9tivier groups.

Abstract

We prove $L^p\to L^q$ estimates for local maximal operators associated with dilates of codimension two spheres in Heisenberg groups; these are sharp up to two endpoints. The results can be applied to improve currently known bounds on sparse domination for global maximal operators. We also consider lacunary variants, and extensions to M\'etivier groups.