Abstract
In this paper, the boundedness of a large class of sublinear commutator operators Tb generated by a Calderon-Zygmund type operator on a generalized weighted Morrey spaces \({M_{p,\varphi }}(w)\) with the weight function w belonging to Muckenhoupt’s class Ap is studied. When 1 < p < ∞ and b ∈ BMO, sufficient conditions on the pair (φ1, φ2) which ensure the boundedness of the operator Tb from \({M_{p,\varphi 1}}(w)\) to \({M_{p,\varphi 2}}(w)\) are found. In all cases the conditions for the boundedness of Tb are given in terms of Zygmund-type integral inequalities on (φ1, φ2), which do not require any assumption on monotonicity of φ1(x, r), φ2(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.
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