Volume 27, Issue 4
The Boundedness of Toeplitz-Type Operators on Vanishing-Morrey Spaces

Anal. Theory Appl., 27 (2011), pp. 309-319.

Published online: 2011-11

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• Abstract

In this note, we prove that the Toeplitz-type Operator $\Theta_\alpha^b$ generated by the generalized fractional integral, Calderón-Zygmund operator and VMO function is bounded from $L^{p,\lambda} (R^n)$ to $L^{q,\mu} (R^n)$. We also show that under some conditions $\Theta_\alpha^b f \in V L^{q,\mu} (B_R)$, the vanishing-Morrey space.

• AMS Subject Headings

42B25, 42B30

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@Article{ATA-27-309, author = {}, title = {The Boundedness of Toeplitz-Type Operators on Vanishing-Morrey Spaces}, journal = {Analysis in Theory and Applications}, year = {2011}, volume = {27}, number = {4}, pages = {309--319}, abstract = {

In this note, we prove that the Toeplitz-type Operator $\Theta_\alpha^b$ generated by the generalized fractional integral, Calderón-Zygmund operator and VMO function is bounded from $L^{p,\lambda} (R^n)$ to $L^{q,\mu} (R^n)$. We also show that under some conditions $\Theta_\alpha^b f \in V L^{q,\mu} (B_R)$, the vanishing-Morrey space.

}, issn = {1573-8175}, doi = {https://doi.org/10.1007/s10496-011-0309-y}, url = {http://global-sci.org/intro/article_detail/ata/4603.html} }
TY - JOUR T1 - The Boundedness of Toeplitz-Type Operators on Vanishing-Morrey Spaces JO - Analysis in Theory and Applications VL - 4 SP - 309 EP - 319 PY - 2011 DA - 2011/11 SN - 27 DO - http://doi.org/10.1007/s10496-011-0309-y UR - https://global-sci.org/intro/article_detail/ata/4603.html KW - Toeplitz-type operator, generalized fractional integral, vanishing-Morrey space. AB -

In this note, we prove that the Toeplitz-type Operator $\Theta_\alpha^b$ generated by the generalized fractional integral, Calderón-Zygmund operator and VMO function is bounded from $L^{p,\lambda} (R^n)$ to $L^{q,\mu} (R^n)$. We also show that under some conditions $\Theta_\alpha^b f \in V L^{q,\mu} (B_R)$, the vanishing-Morrey space.

Xiaoniu Cao & Dongxiang Chen. (1970). The Boundedness of Toeplitz-Type Operators on Vanishing-Morrey Spaces. Analysis in Theory and Applications. 27 (4). 309-319. doi:10.1007/s10496-011-0309-y
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