单位球Bn上的Bohr不等式

数学季刊 ›› 2007, Vol. 22 ›› Issue (2): 159-165.

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单位球Bⁿ上的Bohr不等式

1. Department of Mathematics, University of Science and Technology of China2. Department of Mathematics, Huzhou Teacher's College

收稿日期:2006-12-20 出版日期:2007-06-30 发布日期:2023-11-01
作者简介: WANG Jian-fei(1978-), male, native of Jiangshan, Zhejiang, Ph.D., engages in several complex variables.
基金资助:
Supported by the NNSF of China(10571164); Supported by Specialized Research Fund for the Doctoral Program of Higher Education(SRFDP)(20050358052); Supported by the NSF of Zhejiang Province(Y606197)

Bohr's Inequality on the Unit Ball Bⁿ

1. Department of Mathematics, University of Science and Technology of China2. Department of Mathematics, Huzhou Teacher's College

Received:2006-12-20 Online:2007-06-30 Published:2023-11-01
About author: WANG Jian-fei(1978-), male, native of Jiangshan, Zhejiang, Ph.D., engages in several complex variables.
Supported by:
Supported by the NNSF of China(10571164); Supported by Specialized Research Fund for the Doctoral Program of Higher Education(SRFDP)(20050358052); Supported by the NSF of Zhejiang Province(Y606197)

摘要/Abstract

摘要： Bohr’s type inequalities are studied in this paper: if f is a holomorphic mapping from the unit ball Bⁿ to Bⁿ, f(0)=p, then we have sum from ... and φ_P∈Aut(Bⁿ) such that φ_p=0. As corollaries of the above estimate, we obtain some sharp Bohr’s type modulus inequalities. In particular, when n=1 and |P|→1, then our theorem reduces to a classical result of Bohr.

关键词: Bohr's inequality, holomorphic mapping, homogeneous expansions

Abstract: Bohr’s type inequalities are studied in this paper: if f is a holomorphic mapping from the unit ball Bⁿ to Bⁿ, f(0)=p, then we have sum from ... and φ_P∈Aut(Bⁿ) such that φ_p=0. As corollaries of the above estimate, we obtain some sharp Bohr’s type modulus inequalities. In particular, when n=1 and |P|→1, then our theorem reduces to a classical result of Bohr.

Key words: Bohr's inequality, holomorphic mapping, homogeneous expansions

中图分类号:

O174.52

王建飞, 刘太顺. 单位球Bⁿ上的Bohr不等式[J]. 数学季刊, 2007, 22(2): 159-165.

WANG Jian-fei, LIU Tai-shun. Bohr's Inequality on the Unit Ball Bⁿ[J]. Chinese Quarterly Journal of Mathematics, 2007, 22(2): 159-165.

[1]	刘小松, 刘太顺. 关于局部双全纯映射的推广的Roper-Suffridge算子[J]. 数学季刊, 2003, 18(3): 221-229.
[2]	苏简兵. Extension of Proper μ-holomorphic Mappings[J]. 数学季刊, 1998, 13(3): 59-63.

单位球Bⁿ上的Bohr不等式

Bohr's Inequality on the Unit Ball Bⁿ

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