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.

参考文献

[1] Chen H H, Gauthier P. Boundedness from below of composition operators and $\mu$-Bloch spaces. Canad Math Bull, 2008, 51(2): 195--204

[2] Madigan K. Composition operators on analytic Lipschitz spaces. Proc Amer Math Soc, 1993, 119(2): 465-473

[3] Madigan K, Matheson A. Compact composition operators on the Bloch space. Trans Amer Math Soc, 1995, 347(7): 2679-2687

[4] Zhao R H. Composition operators from Bloch type spaces to Hardy and Besov spaces. J Math Anal Appl, 1999, 233(2): 749-766

[5] Xiao J. Composition operators associated with Bloch-type spaces. Complex Variables Theory Appl, 2001, 46(2): 109-121

[6] Yoneda R. The composition operators on weighted Bloch space. Arch Math(Basel), 2002, 78(4): 310-317

[7] Ohno S, Stroethoff K, Zhao R H. Weighted composition operators between Bloch-type spaces. Rocky Mountain J Math, 2003, 33(1): 191-215

[8] Shi J H, Luo L. Composition operators on the Bloch space of several complex variables. Acta Math Sinica, 2000, 16(1): 85-98

[9] Zhou Z H, Zeng H G. Composition operators between p-Bloch space and q-Bloch space in the unit ball. Progress in Natural Science, 2003, 13(3): 233-236

[10] Zhang X J, Liu J C. Composition operators from spaces F(p,q,s) to Bloch type spaces on the unit ball. Acta Math Sci, 2007, 27A(1): 19--26

[11] Zhang X J. Composition type operator from Bergman space to $\mu$-Bloch type space in Cⁿ. J Math Anal Appl, 2004, 298(2): 710--721

[12] Zhang X J, Liu J C. Composition operators from weighted Bergman spaces to μ-Bloch spaces. Chinese Ann Math, Ser A, 2007, 28(2): 255-266

[13] Zhu K H. Spaces of Holomorphic Functions in the Unit Ball. New York: Springer-Verlag, 2004

[14] Rudin W. Function Theory in the Unit Ball of Cⁿ. New York: Springer-Verlag, 1980

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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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