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.

  • Keywords

Toeplitz type operator, variable Calderon-Zygmund kernel, fractional integral, 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 Calderon-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.

Yuexiang He. (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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