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Volume 35, Issue 4
Weighted Norm Inequalities for Toeplitz Type Operator Related to Singular Integral Operator with Variable Kernel

Yuexiang He

Anal. Theory Appl., 35 (2019), pp. 377-391.

Published online: 2020-01

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  • Abstract

Let $T^{k,1}$ be the singular integrals with variable Calderόn-Zygmund kernels or $\pm I$ (the identity operator), let $T^{k,2}$ and $T^{k,4}$ be the linear operators, and let $T^{k,3}=\pm I$. Denote the Toeplitz type operator by

$$T^b=\sum_{k=1}^t(T^{k,1}M^bI_\alpha T^{k,2}+T^{k,3}I_\alpha M^b T^{k,4}),$$

where $M^bf=bf,$ and $I_\alpha$ is the fractional integral operator. In this paper, we investigate the boundedness of the operator on weighted Lebesgue space when $b$ belongs to weighted Lipschitz space.

  • AMS Subject Headings

42B20, 42B25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

heyuexiang63@163.com (Yuexiang He)

  • BibTex
  • RIS
  • TXT
@Article{ATA-35-377, author = {He , Yuexiang}, title = {Weighted Norm Inequalities for Toeplitz Type Operator Related to Singular Integral Operator with Variable Kernel}, journal = {Analysis in Theory and Applications}, year = {2020}, volume = {35}, number = {4}, pages = {377--391}, abstract = {

Let $T^{k,1}$ be the singular integrals with variable Calderόn-Zygmund kernels or $\pm I$ (the identity operator), let $T^{k,2}$ and $T^{k,4}$ be the linear operators, and let $T^{k,3}=\pm I$. Denote the Toeplitz type operator by

$$T^b=\sum_{k=1}^t(T^{k,1}M^bI_\alpha T^{k,2}+T^{k,3}I_\alpha M^b T^{k,4}),$$

where $M^bf=bf,$ and $I_\alpha$ is the fractional integral operator. In this paper, we investigate the boundedness of the operator on weighted Lebesgue space when $b$ belongs to weighted Lipschitz space.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2018-1012}, url = {http://global-sci.org/intro/article_detail/ata/13618.html} }
TY - JOUR T1 - Weighted Norm Inequalities for Toeplitz Type Operator Related to Singular Integral Operator with Variable Kernel AU - He , Yuexiang JO - Analysis in Theory and Applications VL - 4 SP - 377 EP - 391 PY - 2020 DA - 2020/01 SN - 35 DO - http://doi.org/10.4208/ata.OA-2018-1012 UR - https://global-sci.org/intro/article_detail/ata/13618.html KW - Toeplitz type operator, variable Calderόn-Zygmund kernel, fractional integral, weighted Lipschitz space. AB -

Let $T^{k,1}$ be the singular integrals with variable Calderόn-Zygmund kernels or $\pm I$ (the identity operator), let $T^{k,2}$ and $T^{k,4}$ be the linear operators, and let $T^{k,3}=\pm I$. Denote the Toeplitz type operator by

$$T^b=\sum_{k=1}^t(T^{k,1}M^bI_\alpha T^{k,2}+T^{k,3}I_\alpha M^b T^{k,4}),$$

where $M^bf=bf,$ and $I_\alpha$ is the fractional integral operator. In this paper, we investigate the boundedness of the operator on weighted Lebesgue space when $b$ belongs to weighted Lipschitz space.

He , Yuexiang. (2020). Weighted Norm Inequalities for Toeplitz Type Operator Related to Singular Integral Operator with Variable Kernel. Analysis in Theory and Applications. 35 (4). 377-391. doi:10.4208/ata.OA-2018-1012
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