Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces

In this paper, the boundedness of a large class of sublinear commutator operators T b generated by a Calderón-Zygmund type operator on a generalized weighted Morrey spaces with the weight function w belonging to Muckenhoupt’s class A p is studied. When 1 < p < ∞ and b ∈ BMO, sufficient conditions on the pair ( φ 1 , φ 2 ) which ensure the boundedness of the operator T b from to are found. In all cases the conditions for the boundedness of T b are given in terms of Zygmund-type integral inequalities on ( φ 1 , φ 2 ), which do not require any assumption on monotonicity of φ 1 ( x , r ), φ 2 ( x , r ) in r . Then these results are applied to several particular operators such as the pseudo-differential operators, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.