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The aim of this paper is to get the boundedness of certain sublinearoperators with rough kernel generated by Calder\'on-Zygmund operators on thegeneralized weighted Morrey spaces under generic size conditions which aresatisfied by most of the operators in harmonic analysis. We also prove that thecommutator operators formed by BMO functions and certain sublinear operatorswith rough kernel are also bounded on the generalized weighted Morrey spaces.Marcinkiewicz operator which satisfies the conditions of these theorems can beconsidered as an example.

The boundedness of certain sublinear operators with rough kernel  generated by Calder\'on-Zygmund operators and their commutators on  generalized weighted Morrey spaces