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This paper is devoted to studying the boundedness of multilinear operartorsand their commutators on generalized weighted Morrey spaces, which includesmultilinear fractional maximal operator and multilinear fractional integraloperator. Moreover, we show that two different characterizations for theboundedness of multilinear fractional maximal operators and their commutatorson generalized weighted Morrey spaces under different conditions. As someinportant applications, we give the boundedness of multilinear fractionalintegral operator on generalized weighted Besov-Morrey spaces and also obtaintwo embedding theorems as well as apriori estimates for the sub-Laplacian$\mathcal L$.

Characterizations for multilinear fractional maximal and integral  operators and their commutators on generalized weighted Morrey spaces and  applications