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

Abstract

Abstract In this paper, the main aim is to consider the boundedness of the nonlinear commutator [ b , M α ] $[b, M_{\alpha}]$ and the maximal commutator M α , b $M_{\alpha ,b}$ on the Lebesgue spaces over some stratified Lie group G $\mathbb{G}$ when the symbol b belongs to the Lipschitz space. As a result, some new characterizations of the Lipschitz spaces on Lie group via [ b , M α ] $[b, M_{\alpha}]$ and M α , b $M_{\alpha ,b}$ are given.

Keywords

• Stratified Lie group
• Fractional maximal function
• Lipschitz function
• Commutator