Schatten Class Weighted Composition Operators on the Bergman Space of the Unit Ball

作     者：刘永民 于燕燕 LIU Yong-min;YU Yan-yan

作者机构：徐州师范大学数学系江苏徐州221116 徐州工程学院计算科学系江苏徐州221008 

出 版 物：《Journal of Mathematical Research and Exposition》 (数学研究与评论（英文版）)

年 卷 期：2007年第27卷第3期

页      面：533-538页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：the National Natural Science Foundation of China(10471039) the Natural Science Foundation of the Education Commission of Jiangsu Province(03KJD140210,06KJD110175) the Natural Science Foundation of Xuzhou Institute of Technology(KY200508) 

主　　题：Bergman space weighted composition operator Schatten class Hilbert-Schmidt operator 

摘      要：We consider the Schatten class weighted composition operators on the Bergman space of the unit ball. The main result is several necessary and sutfficient conditions for such kind of weighted composition operators belong to the Schatten-Von Neumann ideal Sp. As a corollary, we now have that Wφ,ψ is a Hilbert-Schmidt operator if and only if ∫Bn │ψ（w）│^2/（1-│φ（W）│^2）^n＋1 dV（W）〈∞