单位球上Hardy空间的加权复合算子  

Weighted composition operators on Hardy spaces of the unit ball

作　　者：胡小浇[1] 于涛[1] 

机构地区：[1]浙江师范大学数理与信息工程学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2009年第3期281-286,共6页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(10771064)

摘　　要：采用泛函分析和复分析方法研究了单位球上Hardy空间的加权复合算子的有界性和紧性.给出了加权复合算子有界的充要条件;加权复合算子Tψ,φ是单位球上的Hardy空间的紧算子,则在球面上|φ|<1几乎处处成立;以及加权复合算子是Hilbert-Schmidt算子的充要条件等结果.所得结果推广和统一了已有文献的相关结果.By using the method of functional analysis and complex analysis, the boundedness and compactness of the weighted composition operators on Hardy spaces of the unit ball were discussed. The necessary and sufficient conditions for bounded weighted composition operators were presented, when the weighted composition operators Tψ,φ is compact operators on Hardy spaces of the unit ball, it was showed that｜ φ｜ 〈 1 almost everywhere on the surface of the unit ball, the necessary and sufficient conditions for weighted composition operators being Hilbert-Schmidt operator were given. The results generalized and unified the relevant results in previous literatures.

关 键 词：HARDY空间 加权复合算子 角导数 Hilbert—Schmidt算子 

分 类 号：O177.1[理学—数学]