Norm inequalities of operators and commutators on generalized weighted morrey spaces

Volume 10, Issue 7, pp 3490--3501 http://dx.doi.org/10.22436/jnsa.010.07.12

Publication Date: July 22, 2017 Submission Date: April 20, 2017

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Authors

Yue Hu - School of Mathematics and Information, Henan Polytechnic University, Jiaozuo 454003, P. R. China. Yueshan Wang - Department of Mathematics, Jiaozuo University, Jiaozuo 454003, P. R. China.

Abstract

We prove that, if a class of operators, which includes singular integral operator with rough kernel, Bochner-Riesz operator and Marcinkiewicz integral operator, are bounded on weighted Lebesgue spaces and satisfy some local pointwise control, then these operators and associated commutators, formed by a BMO function and these operators, are also bounded on generalized weighted Morrey spaces.

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Keywords

• Singular integral with rough kernel
• Bochner-Riesz operator
• Marcinkiewicz integral
• commutator
• weighted Morrey space.

MSC

•  42B35
•  47B38
•  30H35

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