WEIGHTED ESTIMATES FOR VECTOR-VALUED COMMUTATORS OF MULTILINEAR OPERATORS

Abstract

Let $T$ be the multilinear Calderón-Zygmund operator and $T_q(\vec{f})$ be the vector-valued version of $T$ given by $T_q(\vec{f})(x) = \bigg( \sum_{k=1}^\infty |T(f_{1k}, \cdots, f_{mk})(x)|^q\bigg)^{{1}/{q}}$. In this paper, the weighted strong type and weighted end-point weak type estimates for the commutators of $T_q(\vec{f})$ were established respectively.