Boundedness of a Class of Sublinear Operators and Their Commutators on Generalized Morrey Spaces

Vagif S. Guliyev, Seymur S. Aliyev and Turhan Karaman

Abstract and Applied Analysis, 2011, vol. 2011, 1-18

Abstract:

The authors study the boundedness for a large class of sublinear operator generated by Calderón-Zygmund operator on generalized Morrey spaces . As an application of this result, the boundedness of the commutator of sublinear operators on generalized Morrey spaces is obtained. In the case , and is a sublinear operator, we find the sufficient conditions on the pair ( ) which ensures the boundedness of the operator from one generalized Morrey space to another . In all cases, the conditions for the boundedness of are given in terms of Zygmund-type integral inequalities on ( ), which do not assume any assumption on monotonicity of in . Conditions of these theorems are satisfied by many important operators in analysis, in particular pseudodifferential operators, Littlewood-Paley operator, Marcinkiewicz operator, and Bochner-Riesz operator.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:356041

DOI: 10.1155/2011/356041

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