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

Abstract

In this paper, the boundedness of a large class of sublinear commutator operators T (b) generated by a Caldern-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 < a and b a BMO, sufficient conditions on the pair (phi (1), phi (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 (phi (1), phi (2)), which do not require any assumption on monotonicity of phi (1)(x, r), phi (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.