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We prove continuity properties of higher order commutators of fractionaloperators on the multilinear setting, between a product of weighted Lebesguespaces into certain weighted Lipschitz spaces. The considered operators includethe multilinear fractional integral function and the main results extendprevious estimates known for the unweighted case, as well as those establishedon the linear case.  We give a complete study showing the main properties of the relatedmultilinear weights and the optimal region described by the parameters where wecan find nontrivial examples, including the restricted case of the one-weighttheory. We also exhibit examples of such weights on the whole region.

Smoothness properties related to several commutators of fractional  operators for values of $\boldsymbol{p}$ beyond the extreme in the  multilinear setting