Weighted sharp boundedness for multilinear commutators

Abstract

In this paper, the sharp estimates for some multilinear commutators related to certain sublinear integral operators are obtained. The operators include the Littlewood - Paley operator and the Marcinkiewicz operator. As application, we obtain the weighted $L^p (p > 1)$ inequalities and $L \log L$-type estimate for the multilinear commutators.