Commutators of the maximal and sharp functions with weighted Lipschitz functions

Pu Zhang, Xiaomeng Zhu

Let $M$ be the Hardy-Littlewood maximal function. Denote by $M_b$ and $[b,M]$ the maximal and the nonlinear commutators of $M$ with a function $b$. The boundedness of $M_b$ and $[b…