| 单位球的Bergman空间上Schatten类加权复合算子 |
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| 引用本文： | 刘永民,于燕燕.单位球的Bergman空间上Schatten类加权复合算子[J].数学研究及应用,2007,27(3):533-538. |
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| 作者姓名： | 刘永民 于燕燕 |
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| 作者单位： | 1. 徐州师范大学数学系,江苏,徐州,221116
2. 徐州工程学院计算科学系,江苏,徐州,221008 |
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| 基金项目： | 国家自然科学基金;江苏省教育厅自然科学基金 |
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| 摘 要： | 本文研究了单位球的Bergman空间上Schatten类加权复合算子,得到了这种加权复合算子属于Schatten-Von Neumann.理想S_p的几个充要条件.作为推论给出了Wφ,φ是一个Hilbert- Schmidt算子的充要条件是∫_(Bn)(|ψ(ω)|~2)/((1-|φ(ω)|~2)~(n 1)dV(ω)<∞..
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| 关 键 词： | Bergman空间 加权复合算子 Schatten-类 Hilbert-Schmidt算子. |
| 文章编号： | 1000-341X（2007）03-0533-06 |
| 收稿时间： | 2005/11/28 0:00:00 |
| 修稿时间： | 7/2/2006 12:00:00 AM |
Schatten Class Weighted Composition Operators on the Bergman Space of the Unit Ball |
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| LIU Yong-min and YU Yan-yan.Schatten Class Weighted Composition Operators on the Bergman Space of the Unit Ball[J].Journal of Mathematical Research with Applications,2007,27(3):533-538. |
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| Authors: | LIU Yong-min and YU Yan-yan |
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| Institution: | Department of Mathematics, Xuzhou Normal University, Jiangsu 221116, China;Department of Computation Science, Xuzhou Institute of Technology, Jiangsu 221008, China |
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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 $\int_{B_n}\frac{|\psi(w)|^2}{(1-|\varphi(w)|^2)^{n+1}}\d V(w)<\infty.$ |
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| Keywords: | Bergman space weighted composition operator Schatten class Hilbert-Schmidt operator |
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