| Schatten Class Weighted Composition Operators on the Bergman Space of the Unit Ball |
| Received:November 28, 2005 Revised:July 02, 2006 |
| Key Words:
Bergman space weighted composition operator Schatten class Hilbert-Schmidt operator.
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| Fund Project:the National Natural Science Foundation of China (10471039), the Natural Science Foundation of the Education Commission of Jiangsu Province (03KJD140210, 06KJD110175) and the Natural Science Foundation of Xuzhou Institute of Technology (KY200508). |
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| Abstract: |
| We consider the Schatten class weighted composition operators on the Bergman space of the unit ball. The main result is several necessary and sufficient conditions for such kind of weighted composition operators belong to the Schatten-Von Neumann ideal $S_p$. As a corollary, we now have that $W_{\varphi, \psi}$ is a Hilbert-Schmidt operator if and only if $$\int_{B_n}\frac{|\psi(w)|^2}{(1-|\varphi(w)|^2)^{n+1}}\d V(w)<\infty.$$ |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2007.03.012 |
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