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

Y. He & Y. Wang

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 variablekernels 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 thispaper, the boundedness of $T^b$ on weighted Morrey space areobtained when $b$ belongs to the weighted Lipschitz function spaceand weighted BMO function space, respectively.
  • Keywords

Toeplitz type operator singular integral operator variable Calder\'on-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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@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 variablekernels 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 thispaper, the boundedness of $T^b$ on weighted Morrey space areobtained when $b$ belongs to the weighted Lipschitz function spaceand 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 KW - singular integral operator KW - variable Calder\'on-Zygmund kernel KW - weighted BMO function KW - weighted Lipschitz function KW - weighted Morrey space AB - Suppose $T^{k,1}$ and $T^{k,2}$ are singular integrals with variablekernels 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 thispaper, the boundedness of $T^b$ on weighted Morrey space areobtained when $b$ belongs to the weighted Lipschitz function spaceand weighted BMO function space, respectively.
Y. He & Y. Wang. (1970). 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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