Multiple weighted estimates for commutators of multilinear maximal function

Abstract

Let M be the multilinear maximal function and $\vec b$ = (b 1,..., b m ) be a collection of locally integrable functions. Denote by M $\vec b$ and $\vec b$ , M] the maximal commutator and the commutator of M with $\vec b$ , respectively. In this paper, the multiple weighted strong and weak type estimates for operators M $\vec b$ and [ $\vec b$ , M] are studied. Some characterizations of the class of functions b j are given, for which these operators satisfy some strong or weak type estimates.