Norm inequalities of operators and commutators on generalized weighted morrey spaces

We prove that, if a class of operators, which includes singular integral operator with rough kernel, Bochner-Riesz operator and Marcinkiewicz integral operator, are bounded on weighted Lebesgue spaces and satisfy some local pointwise control, then these operators and associated commutators, formed by a BMO function and these operators, are also bounded on generalized weighted Morrey spaces.