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The main questions raised in this paper are to find the sufficient conditionsthat make multi-sublinear operators $T$ and their commutators ${T_{\prod \vec b}}$, ${T_{\sum {\vec b} }}$ to be bounded on three kinds of generalizedweighted Morrey spaces. We give the main theorems of this paper to solve theabove related questions. As corollaries of the main theorems, we givesufficient and necessary conditions for a class of multi-sublinear operatorswhich are bounded on three kinds of generalized weighted Morrey spaces. As someinportant applications, we apply the main results to the multilinearvector-valued Calder\'on-Zygmund operators, multilinear Littlewood-Paley squareoperators, multilinear pseudo-differential operators and multilinearparaproducts.

Characterizations for multi-sublinear operators and their commutators on three kinds of generalized weighted Morrey spaces and applications