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We deal with the boundedness of the multilinear fractional integral operator$I_{\gamma,m}$ from a product of weighted Lebesgue spaces into adequateweighted Lipschitz spaces. Our results generalize some previous estimates notonly for the linear case but also for the unweighted problem in the multilinearcontext. We characterize the classes of weights for which the problem describedabove holds and show the optimal range of the parameters involved. Theoptimality is understood in the sense that the parameters defining thecorresponding spaces belong to a certain region. We further exhibit examples ofweights for the class which cover the mentioned area.

Optimal parameters related with continuity properties of the multilinear fractional integral operator between Lebesgue and Lipschitz spaces