Characterization of Lipschitz Functions via the Commutators of Maximal Function 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.