Hardy空间与Bergman空间之间的向量值复合算子

王茂发;刘培德;

数学学报 ›› 2009 ›› Issue (04) : 79-88.

数学学报 ›› 2009 ›› Issue (04) : 79-88. DOI: 10.12386/A2009sxxb0086
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Hardy空间与Bergman空间之间的向量值复合算子

    王茂发;刘培德;
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Vector-Valued Composition Operators Between Hardy and Bergman Spaces

    Mao Fa WANG Pei De LIU College of Mathematics and Statistics,Wuhan University,Wuhan 430072,P.R.China
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摘要

设φ是从多圆柱D~m到多圆柱D~n或从多圆柱D~m到单位球B_n的全纯映射,X是一无穷维复Banach空间.本文研究了X-值Hardy空间与Bergman空间之间的复合算子,给出了向量值复合算子C_φ有界性的完全刻画.

Abstract

Let φ be a holomorphic mapping from the polydisk D~m into the polydisk Dn,or from the polydisk D~m into the unit ball Bn,and X an infinite dimensional complex Banach space.In this paper,we study the action of the associated composition operator C_φbetween vector-valued Hardy and Bergman spaces defined on D~n or B_n. Some sufficient and necessary conditions for such composition operators to be bounded are obtained.

关键词

向量值全纯函数 / Hardy空间 / Bergman空间 / 复合算子

Key words

Bergman space / composition operator / vector-valued holomorphic function / Hardy space

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王茂发;刘培德;. Hardy空间与Bergman空间之间的向量值复合算子. 数学学报, 2009(04): 79-88 https://doi.org/10.12386/A2009sxxb0086
Mao Fa WANG Pei De LIU College of Mathematics and Statistics,Wuhan University,Wuhan 430072,P.R.China. Vector-Valued Composition Operators Between Hardy and Bergman Spaces. Acta Mathematica Sinica, Chinese Series, 2009(04): 79-88 https://doi.org/10.12386/A2009sxxb0086

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