Boundedness for the Singular Integral with Variable Kernel and Fractional Differentiation on Weighted Morrey Spaces

doi:10.4208/ata.2016.v32.n3.1

Boundedness for the Singular Integral with Variable Kernel and Fractional Differentiation on Weighted Morrey Spaces

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Year: 2016

Analysis in Theory and Applications, Vol. 32 (2016), Iss. 3 : pp. 205–214

Abstract

Let $T$ be the singular integral operator with variable kernel, $T^*$ be the adjoint of $T$ and $T^{\sharp}$ be the pseudo-adjoint of $T$ . Let $T_1T_2$ be the product of $T_1$ and $T_2,$ $T_1\circ T_2$ be the pseudo product of $T_1$ and $T_2.$ In this paper, we establish the boundedness for commutators of these operators and the fractional differentiation operator $D^\gamma$ on the weighted Morrey spaces.

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Journal Article Details

Publisher Name: Global Science Press

Language: English

DOI: https://doi.org/10.4208/ata.2016.v32.n3.1

Analysis in Theory and Applications, Vol. 32 (2016), Iss. 3 : pp. 205–214

Published online: 2016-01

AMS Subject Headings: Global Science Press

Pages: 10

Keywords: Singular integral variable kernel fractional differentiation BMO Sobolev space weighted Morrey spaces.

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