Weighted Inequalities for Multilinear Potential Operators and their Commutators

We prove weighted strong inequalities for the multilinear potential operator T-phi and its commutator, where the kernel phi 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 M-phi,M-LB associated to an essentially nondecreasing function phi and to the Orlicz space L-B for a given Young function B. This result allows us to obtain a weighted weak type inequality for the operator T-phi.