Strong maximal function revisit on Heisenberg group

TL;DR

This paper establishes the boundedness of a strong maximal operator on the Heisenberg group for certain measures, extending harmonic analysis tools to non-commutative settings.

Contribution

It proves the $L^p$-boundedness of the strong maximal operator on the Heisenberg group with measures satisfying the $A_$-property, a novel extension in harmonic analysis.

Findings

Proves $L^p$-boundedness of the strong maximal operator on the Heisenberg group.

Extends classical maximal function results to non-commutative groups.

Uses measures satisfying the product $A_$-property for analysis.

Abstract

We prove the $L^p$-boundedness of the strong maximal operator defined on a Heisenberg group w.r.t an absolutely continuous measure satisfying the product $A_\infty$-property.