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

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.

arXiv admin note: substantial text overlap with arXiv:2205.06529; Journal of Inequalities and Applications(accepted)