Characterization of Lipschitz Functions via the Commutators of Maximal Function on Stratified Lie Groups

TL;DR

This paper investigates the boundedness of certain maximal commutators on Lebesgue and Morrey spaces over stratified Lie groups, providing new characterizations of Lipschitz spaces in this setting.

Contribution

It introduces novel characterizations of Lipschitz spaces on stratified Lie groups via boundedness properties of maximal commutators.

Findings

Boundedness of Hardy-Littlewood maximal commutator $M_b$ on Lebesgue and Morrey spaces.

Boundedness of nonlinear commutator $[b, M]$ on these spaces.

New characterizations of Lipschitz spaces on stratified Lie groups.

Abstract

In this paper, the main aim is to consider the boundedness of the Hardy-Littlewood maximal commutator $M_{b}$ and the nonlinear commutator $[b, M]$ on the Lebesgue spaces and Morrey spaces over some stratified Lie group $\mathbb{G}$ when $b$ belongs to the Lipschitz space, by which some new characterizations of the Lipschitz spaces on Lie group are given.