Multiple weighted estimates for commutators of multilinear maximal function

Let M be the multilinear maximal function and b. = (b 1,..., b m ) be a collection of locally integrable functions. Denote by M b. and b. , M] the maximal commutator and the commutator of M with b. , respectively. In this paper, the multiple weighted strong and weak type estimates for operators M b. and [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.