Weighted Inequalities for Multilinear Potential Operators and their Commutators

Abstract

We prove weighted strong inequalities for the multilinear potential operator T φ and its commutator, where the kernel φ satisfies certain growth condition. For these operators we also obtain Fefferman-Stein type inequalities and Coifman type estimates. Moreover we prove weighted weak type inequalities for the multilinear maximal operator Mϕ,LB associated to an essentially nondecreasing function ϕ and to the Orlicz space LB for a given Young function B. This result allows us to obtain a weighted weak type inequality for the operator Tφ.