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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

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

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.

  • Keywords

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

  • AMS Subject Headings

42B20, 42B25

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{ATA-32-205, author = {C. Xue, K. Zhu and Y. P. Chen}, 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 AU - C. Xue, K. Zhu & Y. P. Chen 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 and Y. P. Chen. (2016). 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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