TWO GENERALIZATIONS OF BOHR RADIUS*

doi:10.1007/s10473-023-0206-4

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (2): 583-596.doi: 10.1007/s10473-023-0206-4

TWO GENERALIZATIONS OF BOHR RADIUS^*

Chengpeng Li, Mingxin Chen, Jianfei Wang^†

School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

收稿日期:2022-03-30 修回日期:2022-06-28 出版日期:2023-03-25 发布日期:2023-04-12
通讯作者: †Jianfei WANG, wangjf@mail.ustc.edu.cn.
作者简介:Chengpeng Li, E-mail: 1319610027@qq.com; Mingxin Chen, E-mail: chernmx@hqu.edu.cn
基金资助:
The project was supported by the National Natural Science Foundation of China (12071161, 11971165 & 11671362) and the Natural Science Foundation of Fujian Province (2020J01073).

TWO GENERALIZATIONS OF BOHR RADIUS^*

Chengpeng Li, Mingxin Chen, Jianfei Wang^†

School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

Received:2022-03-30 Revised:2022-06-28 Online:2023-03-25 Published:2023-04-12
Contact: †Jianfei WANG, wangjf@mail.ustc.edu.cn.
About author:Chengpeng Li, E-mail: 1319610027@qq.com; Mingxin Chen, E-mail: chernmx@hqu.edu.cn
Supported by:
The project was supported by the National Natural Science Foundation of China (12071161, 11971165 & 11671362) and the Natural Science Foundation of Fujian Province (2020J01073).

摘要/Abstract

摘要： The purpose of this paper is twofold. First, by using the hyperbolic metric, we establish the Bohr radius for analytic functions from shifted disks containing the unit disk $D$ into convex proper domains of the complex plane. As a consequence, we generalize the Bohr radius of Evdoridis, Ponnusamy and Rasila based on geometric idea. By introducing an alternative multidimensional Bohr radius, the second purpose is to obtain the Bohr radius of higher dimensions for Carathéodory families in the unit ball $B$ of a complex Banach space $X$. Notice that when $B$ is the unit ball of the complex Hilbert space $X$, we show that the constant $ {1}/{3} $ is the Bohr radius for normalized convex mappings of $B$, which generalizes the result of convex functions on $D$.

关键词: Bohr radius, hyperbolic metric, holomorphic mapping, convex mapping

Abstract: The purpose of this paper is twofold. First, by using the hyperbolic metric, we establish the Bohr radius for analytic functions from shifted disks containing the unit disk $D$ into convex proper domains of the complex plane. As a consequence, we generalize the Bohr radius of Evdoridis, Ponnusamy and Rasila based on geometric idea. By introducing an alternative multidimensional Bohr radius, the second purpose is to obtain the Bohr radius of higher dimensions for Carathéodory families in the unit ball $B$ of a complex Banach space $X$. Notice that when $B$ is the unit ball of the complex Hilbert space $X$, we show that the constant $ {1}/{3} $ is the Bohr radius for normalized convex mappings of $B$, which generalizes the result of convex functions on $D$.

Key words: Bohr radius, hyperbolic metric, holomorphic mapping, convex mapping

Chengpeng Li, Mingxin Chen, Jianfei Wang. TWO GENERALIZATIONS OF BOHR RADIUS^*[J]. 数学物理学报(英文版), 2023, 43(2): 583-596.

Chengpeng Li, Mingxin Chen, Jianfei Wang. TWO GENERALIZATIONS OF BOHR RADIUS^*[J]. Acta mathematica scientia,Series B, 2023, 43(2): 583-596.

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TWO GENERALIZATIONS OF BOHR RADIUS^*

TWO GENERALIZATIONS OF BOHR RADIUS^*

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