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Volume 32, Issue 1
Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces

Y. He & Y. Wang

DOI: 10.4208/ata.2016.v32.n1.8

Anal. Theory Appl., 32 (2016), pp. 90-102.

Published online: 2016-01

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  • Abstract

Suppose $T^{k,1}$ and $T^{k,2}$ are singular integrals with variable kernels and mixed homogeneity or $\pm I$ (the identity operator). Denote the Toeplitz type operator by\begin{align*}T^b=\sum_{k=1}^QT^{k,1}M^bT^{k,2}, \end{align*} where $M^bf=bf.$ In this paper, the boundedness of $T^b$ on weighted Morrey space are obtained when $b$ belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.

  • Keywords

Toeplitz type operator, singular integral operator, variable Calderόn-Zygmund kernel, weighted BMO function, weighted Lipschitz function, weighted Morrey space.

  • AMS Subject Headings

42B20, 40B35

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{ATA-32-90, author = {Y. He and Y. Wang}, title = {Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces}, journal = {Analysis in Theory and Applications}, year = {2016}, volume = {32}, number = {1}, pages = {90--102}, abstract = {

Suppose $T^{k,1}$ and $T^{k,2}$ are singular integrals with variable kernels and mixed homogeneity or $\pm I$ (the identity operator). Denote the Toeplitz type operator by\begin{align*}T^b=\sum_{k=1}^QT^{k,1}M^bT^{k,2}, \end{align*} where $M^bf=bf.$ In this paper, the boundedness of $T^b$ on weighted Morrey space are obtained when $b$ belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2016.v32.n1.8}, url = {http://global-sci.org/intro/article_detail/ata/4657.html} }
TY - JOUR T1 - Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces AU - Y. He & Y. Wang JO - Analysis in Theory and Applications VL - 1 SP - 90 EP - 102 PY - 2016 DA - 2016/01 SN - 32 DO - http://doi.org/10.4208/ata.2016.v32.n1.8 UR - https://global-sci.org/intro/article_detail/ata/4657.html KW - Toeplitz type operator, singular integral operator, variable Calderόn-Zygmund kernel, weighted BMO function, weighted Lipschitz function, weighted Morrey space. AB -

Suppose $T^{k,1}$ and $T^{k,2}$ are singular integrals with variable kernels and mixed homogeneity or $\pm I$ (the identity operator). Denote the Toeplitz type operator by\begin{align*}T^b=\sum_{k=1}^QT^{k,1}M^bT^{k,2}, \end{align*} where $M^bf=bf.$ In this paper, the boundedness of $T^b$ on weighted Morrey space are obtained when $b$ belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.

Y. He and Y. Wang. (2016). Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces. Analysis in Theory and Applications. 32 (1). 90-102. doi:10.4208/ata.2016.v32.n1.8
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