  Given an $m$-tuple of weights $\vec{v}=(v_1,\dots,v_m)$, we characterize the
classes of pairs $(w,\vec{v})$ involved with the boundedness properties of the
multilinear fractional integral operator from
$\prod_{i=1}^mL^{p_i}\left(v_i^{p_i}\right)$ into suitable Lipschitz spaces
associated to a parameter $\delta$, $\mathcal{L}_w(\delta)$. Our results
generalize some previous estimates not only for the linear case but also for
the unweighted problem in the multilinear context. We emphasize the study
related to the range of the parameters involved with the problem described
above, which is optimal in the sense that they become trivial outside of the
region obtained.
  We also exhibit nontrivial examples of pairs of weights in this region.
