  We deal with the boundedness of the multilinear fractional integral operator
$I_{\gamma,m}$ from a product of weighted Lebesgue spaces into adequate
weighted Lipschitz spaces. Our results generalize some previous estimates not
only for the linear case but also for the unweighted problem in the multilinear
context. We characterize the classes of weights for which the problem described
above holds and show 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. We further exhibit examples of
weights for the class which cover the mentioned area.
