  This paper is devoted to studying the boundedness of multilinear operartors
and their commutators on generalized weighted Morrey spaces, which includes
multilinear fractional maximal operator and multilinear fractional integral
operator. Moreover, we show that two different characterizations for the
boundedness of multilinear fractional maximal operators and their commutators
on generalized weighted Morrey spaces under different conditions. As some
inportant applications, we give the boundedness of multilinear fractional
integral operator on generalized weighted Besov-Morrey spaces and also obtain
two embedding theorems as well as apriori estimates for the sub-Laplacian
$\mathcal L$.
