多圆盘上的H∞与广义加权Bloch空间之间的复合算子

数学物理学报 ›› 2009, Vol. 29 ›› Issue (6): 1634-1641.

多圆盘上的H^∞与广义加权Bloch空间之间的复合算子

河南师范大学数学与信息科学学院河南新乡 453007

收稿日期:2007-12-25 修回日期:2008-12-18 出版日期:2009-12-25 发布日期:2009-12-25
基金资助:
国家自然科学基金(10671147), 教育部科学技术研究重点项目(208081)和河南省自然科学基金(2008110006)资助

Composition Operators Between H^∞ and Generally Weighted Bloch Spaces in Polydisk

College of Mathematics and Information Science, Henan Normal University, Henan Xinxiang 453007

Received:2007-12-25 Revised:2008-12-18 Online:2009-12-25 Published:2009-12-25
Supported by:
国家自然科学基金(10671147), 教育部科学技术研究重点项目(208081)和河南省自然科学基金(2008110006)资助

摘要/Abstract

摘要：

设 φ 是Cⁿ的开单位多圆盘上的全纯自映射, α > 0. 该文主要研究了多圆盘上的H^∞与广义加权Bloch空间B^α_log(Uⁿ)之间的复合算子C_φ的有界性与紧性.

关键词: 全纯自映射, 复合算子, 广义加权Bloch空间

Abstract:

Let φ be a holomorphic self-map of the open unit polydisk Uⁿ in Cⁿ and α > 0. In this article, the boundedness and compactness of composition operator C_φ between H^∞ and generally weighted Bloch space B^α_log in polydisk are investigated.

Key words: Holomorphic self-map, Composition operator, Generally weighted Bloch space

中图分类号:

47B38

李海英, 刘培德. 多圆盘上的H^∞与广义加权Bloch空间之间的复合算子[J]. 数学物理学报, 2009, 29(6): 1634-1641.

LI Hai-Ying, LIU Pei-De. Composition Operators Between H^∞ and Generally Weighted Bloch Spaces in Polydisk[J]. Acta mathematica scientia,Series A, 2009, 29(6): 1634-1641.

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