  We prove continuity properties of higher order commutators of fractional
operators on the multilinear setting, between a product of weighted Lebesgue
spaces into certain weighted Lipschitz spaces. The considered operators include
the multilinear fractional integral function and the main results extend
previous estimates known for the unweighted case, as well as those established
on the linear case.
  We give a complete study showing the main properties of the related
multilinear weights and the optimal region described by the parameters where we
can find nontrivial examples, including the restricted case of the one-weight
theory. We also exhibit examples of such weights on the whole region.
