Multiple Weighted Estimates for Commutators of Multilinear Maximal Function

Let M be the multilinear maximal function and = （b1, . . . , bm） be a collection of locally integrable functions. Denote by M and [,M] the maximal commutator and the commutator of M with , respectively. In this paper, the multiple weighted strong and weak type estimates for operators M and [,M] are studied. Some characterizations of the class of functions bj are given, for which these operators satisfy some strong or weak type estimates.