Weighted estimates for commutators of vector-valued maximal multilinear operators

Let T∗T∗ be the maximal multilinear Calderón–Zygmund operator defined by T∗(f→)(x)=supδ>0|Tδ(f1,…,fm)(x)|, and Tq∗(f→) be the vector-valued version of T∗T∗, Tq∗(f→)(x)=(∑k=1∞|T∗(f1k,…,fmk)(x)|q)1/q, where TδTδ are the smooth truncations of the multilinear singular integral operator TT. In this paper, we consider weighted norm inequalities for the iterated commutators of vector-valued maximal multilinear operators Tq∗(f→). The weighted strong type and weighted end-point weak type estimates for the iterated commutators of Tq∗(f→) were established respectively.