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Volume 32, Issue 3
Boundedness for the Singular Integral with Variable Kernel and Fractional Differentiation on Weighted Morrey Spaces

C. Xue, K. Zhu & Y. P. Chen

Anal. Theory Appl., 32 (2016), pp. 205-214.

Published online: 2016-07

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  • 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.

  • AMS Subject Headings

42B20, 42B25

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COPYRIGHT: © Global Science Press

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@Article{ATA-32-205, author = {}, title = {Boundedness for the Singular Integral with Variable Kernel and Fractional Differentiation on Weighted Morrey Spaces}, journal = {Analysis in Theory and Applications}, year = {2016}, volume = {32}, number = {3}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2016.v32.n3.1}, url = {http://global-sci.org/intro/article_detail/ata/4666.html} }
TY - JOUR T1 - Boundedness for the Singular Integral with Variable Kernel and Fractional Differentiation on Weighted Morrey Spaces JO - Analysis in Theory and Applications VL - 3 SP - 205 EP - 214 PY - 2016 DA - 2016/07 SN - 32 DO - http://doi.org/10.4208/ata.2016.v32.n3.1 UR - https://global-sci.org/intro/article_detail/ata/4666.html KW - Singular integral, variable kernel, fractional differentiation, BMO Sobolev space, weighted Morrey spaces. AB -

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.

C. Xue, K. Zhu & Y. P. Chen. (1970). Boundedness for the Singular Integral with Variable Kernel and Fractional Differentiation on Weighted Morrey Spaces. Analysis in Theory and Applications. 32 (3). 205-214. doi:10.4208/ata.2016.v32.n3.1
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