从双曲α-Bloch 空间到双曲{\boldmath QK型空间上的复合算子

数学物理学报 ›› 2009, Vol. 29 ›› Issue (5): 1311-1320.

从双曲α-Bloch 空间到双曲{\boldmath Q_K型空间上的复合算子

1.徐州工程学院数学与物理科学学院江苏徐州 221008|2.徐州师范大学数学科学学院江苏徐州 221116

收稿日期:2007-06-11 修回日期:2009-03-15 出版日期:2009-10-25 发布日期:2009-10-25
基金资助:
国家自然科学基金(10471039)、江苏省普通高校自然科学研究计划资助项目(06KJD110175, 07KJB110115)和徐州工程学院培育课题(XKY2008310)资助

Composition Operators from Hyperbolic α-Bloch Spaces into Hyperbolic Q_K Type Spaces

1.School of Mathematics and Physics |Science, Xuzhou Institute of Technology, Jiangsu Xuzhou 221008|2.Department of Mathematics, Xuzhou Normal University, Jiangsu Xuzhou 221116

Received:2007-06-11 Revised:2009-03-15 Online:2009-10-25 Published:2009-10-25
Supported by:
国家自然科学基金(10471039)、江苏省普通高校自然科学研究计划资助项目(06KJD110175, 07KJB110115)和徐州工程学院培育课题(XKY2008310)资助

摘要/Abstract

摘要：

若 φ 为单位圆盘D上的解析自映射, X为D上解析函数全体构成的Banach空间. 定义X上复合算子C_φ: C_φ (f)=f ο φ , 对任意 f ∈ X. 该文研究了从双曲α-Bloch 空间到双曲Q_K型空间上复合算子的有界性的特征. 另外, 还给出了从 D_p, α 到Q_K(p, q) 空间上复合算子的有界性和紧性的特征.

关键词: 复合算子, 解析函数, 加权Dirichlet 空间

Abstract:

Suppose φ is an analytic map of the unit disk D into itself, X is a Banach space of analytic functions on D.
Define the composition operator C_φ: C_φ(f)=f ο φ , for all f ∈ X. In this paper, the boundedness of the composition operators from hyperbolic α-Bloch spaces into hyperbolic Q_K type spaces are discussed, where 0 < α ≤ 1. Moreover, a necessary and sufficient condition for C_φ from weighted Dirichlet space D_p, αto Q_K(p, q) to be bounded or compact is given in terms of the map φ.

Key words: Composition operator, Analytic function, Weighted Dirichlet space

中图分类号:

47B38

于燕燕, 刘永民. 从双曲α-Bloch 空间到双曲{\boldmath Q_K型空间上的复合算子[J]. 数学物理学报, 2009, 29(5): 1311-1320.

YU Yan-Yan, LIU Yong-Min. Composition Operators from Hyperbolic α-Bloch Spaces into Hyperbolic Q_K Type Spaces[J]. Acta mathematica scientia,Series A, 2009, 29(5): 1311-1320.

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