Some estimates for commutators of the fractional maximal function on stratified Lie groups

TL;DR

This paper investigates the boundedness of fractional maximal commutators on Lebesgue spaces over stratified Lie groups, providing new characterizations of Lipschitz spaces within this mathematical context.

Contribution

It introduces new results on the boundedness of fractional maximal commutators and offers novel characterizations of Lipschitz spaces on stratified Lie groups.

Findings

Boundedness results for fractional maximal commutators on Lebesgue spaces.

New characterizations of Lipschitz spaces on stratified Lie groups.

Analysis of nonlinear commutators in the Lie group setting.

Abstract

In this paper, the main aim is to consider the boundedness of the fractional maximal commutator $M_{\alpha,b}$ and the nonlinear commutator $[b, M_{\alpha}]$ on the Lebesgue 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.