Weighted estimates for lacunary maximal functions on homogeneous groups

TL;DR

This paper investigates weighted bounds for lacunary maximal functions on homogeneous groups, providing improved estimates for specific spherical maximal functions in the Heisenberg group and related settings.

Contribution

It introduces new weighted estimates for lacunary maximal functions on homogeneous groups, including applications to Korányi spherical means and spheres in the Heisenberg group.

Findings

Improved weighted estimates for Korányi spherical means.

Enhanced bounds for lacunary maximal functions in the Heisenberg group.

Generalization of weighted inequalities to broader classes of homogeneous groups.

Abstract

In this article, we study weighted estimates for a general class of lacunary maximal functions on homogeneous groups. As an application we derive improved weighted estimates for the lacunary maximal function associated to the Kor\'anyi spherical means as well as for the lacunary maximal function associated to codimension two spheres in the Heisenberg group.