多圆柱上的Bloch空间上的加权复合算子  

WEIGHTED COMPOSITION OPERATORS ON THE BLOCH SPACE IN POLYDISCS

作　　者：周泽华[1] 魏中齐[1] 

机构地区：[1]天津大学数学系,天津300072

出　　处：《数学杂志》2005年第4期435-440,共6页Journal of Mathematics

基　　金：国家自然科学基金资助(10371091);南开大学天津大学刘徽应用数学中心资助.

摘　　要：利用泛函分析多复变方法,研究了多圆柱上Bloch空间的加权复合算子的一些性质.并且通过圆柱的全纯自映射及全纯函数ψ的一些特性,分别给出了多圆柱上Bloch空间上由及ψ确定的加权复合算子的有界性与紧性的充要条件.By the methods of function analysis and several complex variables,some properties of weighted composition operator in the Bloch space in the unit polydisk are studied in this paper. In terms of the properties of the holomorphic self-map  and holomorphic function ψ, the sufficient and necessary conditions are given for the weighted composition operator induced by  and ψ to be bounded and compact on the Bloch space in polydisic.

关 键 词：多圆柱 BLOCH空间 复合算子 紧复合算子 BERGMAN度量 

分 类 号：O174.56[理学—数学]