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In this paper, we obtain bounded criteria on certain weighted Morrey spaces for the commutators generalized by some sublinear integral operators and weighted Lipschitz functions. We also present bounded criteria for commutators generalized by such sublinear integral operators and weighted BMO function on the weighted Morrey spaces. As applications, our results yield the same bounded criteria for those commutators on the classical weighted Morrey spaces.

Boundedness criteria for commutators of some sublinear operators in weighted Morrey spaces