COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL

doi:10.1016/S0252-9602(09)60115-6

数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (5): 1430-1438.doi: 10.1016/S0252-9602(09)60115-6

COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL

王雄亮, 刘太顺

Department of Mathematics, University of Science and Technology of China, Hefei 230026, |China Department of Mathematics, Huzhou Teachers College, Huzhou, Zhejiang 313000, China

收稿日期:2006-09-10 修回日期:2007-08-07 出版日期:2009-09-20 发布日期:2009-09-20
基金资助:
Supported by NSF of China (10571164) and SRFDP of Higher Education (20050358052)

COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL

WANG Xiong-Liang, LIU Ta-Shun

Department of Mathematics, University of Science and Technology of China, Hefei 230026, |China Department of Mathematics, Huzhou Teachers College, Huzhou, Zhejiang 313000, China

Received:2006-09-10 Revised:2007-08-07 Online:2009-09-20 Published:2009-09-20
Supported by:
Supported by NSF of China (10571164) and SRFDP of Higher Education (20050358052)

摘要/Abstract

摘要：

Let φ be a holomorphic self-map of B_n and Ψ ∈ H(B_n). A composition type operator is defined by T_Ψ, φ(f)= Ψf ο φ for f ∈ H(B_n), which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator T_Ψ_, φ to be bounded or compact from Hardy space H_p(B_n) to μ-Bloch space B(_Bn). The conditions are some supremums concerned with Ψ, φ, their derivatives and Bergman metric of $\Bn$. At the same time, two corollaries are obtained.

关键词: Hardy spaces, Bloch spaces, composition type operators, boundedness, compactness

Abstract:

Let φ be a holomorphic self-map of B_n and Ψ ∈ H(B_n). A composition type operator is defined by T_Ψ, φ(f)= Ψf ο φ for f ∈ H(B_n), which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator T_Ψ_, φ to be bounded or compact from Hardy space H_p(B_n) to μ-Bloch space B(B_n). The conditions are some supremums concerned with Ψ, φ, their derivatives and Bergman metric of $\Bn$. At the same time, two corollaries are obtained.

Key words: Hardy spaces, μBloch spaces, composition type operators, boundedness, compactness

中图分类号:

47B33

王雄亮, 刘太顺. COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL[J]. 数学物理学报(英文版), 2009, 29(5): 1430-1438.

WANG Xiong-Liang, LIU Ta-Shun. COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL[J]. Acta mathematica scientia,Series B, 2009, 29(5): 1430-1438.

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COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL

COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL

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