  We deal with the boundedness properties of higher order commutators related
to some generalizations of the multilinear fractional integral operator of
order $m$, $I_\alpha ^m$, from a product of weighted Lebesgue spaces into
adequate weighted Lipschitz spaces, extending some previous estimates for the
linear case. Our study includes two different types of commutators and
sufficient conditions on the weights in order to guarantee the continuity
properties described above. We also exhibit the optimal range of the parameters
involved. The optimality is understood in the sense that the parameters
defining the corresponding spaces belong to a certain region, being the weights
trivial outside of it. We further show examples of weights for the class which
cover the mentioned area.
