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We deal with the boundedness properties of higher order commutators relatedto some generalizations of the multilinear fractional integral operator oforder $m$, $I_\alpha ^m$, from a product of weighted Lebesgue spaces intoadequate weighted Lipschitz spaces, extending some previous estimates for thelinear case. Our study includes two different types of commutators andsufficient conditions on the weights in order to guarantee the continuityproperties described above. We also exhibit the optimal range of the parametersinvolved. The optimality is understood in the sense that the parametersdefining the corresponding spaces belong to a certain region, being the weightstrivial outside of it. We further show examples of weights for the class whichcover the mentioned area.

Some extensions of classes involving pair of weights related to the  boundedness of multilinear commutators associated to generalized fractional  integral operators