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

Author

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  • Vagif S. Guliyev
  • Seymur S. Aliyev
  • Turhan Karaman

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.

Suggested Citation

  • Vagif S. Guliyev & Seymur S. Aliyev & Turhan Karaman, 2011. "Boundedness of a Class of Sublinear Operators and Their Commutators on Generalized Morrey Spaces," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-18, July.
    • Handle: RePEc:hin:jnlaaa:356041
    DOI: 10.1155/2011/356041
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    Cited by:

    1. Hua Wang, 2014. "Vector-Valued Inequalities in the Morrey Type Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-15, May.

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