REFINED BOHR INEQUALITIES AND A REFINED BOHR-ROGOSINSKI INEQUALITY ON COMPLEX BANACH SPACES

doi:10.1007/s10473-026-0102-9

数学物理学报(英文版) ›› 2026, Vol. 46 ›› Issue (1): 19-38.doi: 10.1007/s10473-026-0102-9

REFINED BOHR INEQUALITIES AND A REFINED BOHR-ROGOSINSKI INEQUALITY ON COMPLEX BANACH SPACES

Molla Basir AHAMED¹, Sabir AHAMMED¹, Hidetaka HAMADA^2,*

1. Department of Mathematics, Jadavpur University, Kolkata-700032, West Bengal, India;
2. Faculty of Science and Engineering, Kyushu Sangyo University, 3-1 Matsukadai 2-Chome Higashi-Ku, Fukuoka 813-8503, Japan

收稿日期:2024-07-25 修回日期:2024-10-29 出版日期:2026-01-25 发布日期:2026-05-22

REFINED BOHR INEQUALITIES AND A REFINED BOHR-ROGOSINSKI INEQUALITY ON COMPLEX BANACH SPACES

Molla Basir AHAMED¹, Sabir AHAMMED¹, Hidetaka HAMADA^2,*

1. Department of Mathematics, Jadavpur University, Kolkata-700032, West Bengal, India;
2. Faculty of Science and Engineering, Kyushu Sangyo University, 3-1 Matsukadai 2-Chome Higashi-Ku, Fukuoka 813-8503, Japan

Received:2024-07-25 Revised:2024-10-29 Online:2026-01-25 Published:2026-05-22
Contact: * Hidetaka HAMADA, E-mail: h.hamada@ip.kyusan-u.ac.jp
About author:Molla Basir AHAMED,E-mail: E-mail: mbahamed.math@jadavpuruniversity.in; Sabir AHAMMED, E-mail: sabira.math.rs@jadavpuruniversity.in
Supported by:
The first author was supported by the SERB, SUR/2022/002244, Govt. India and the second author was supported by the UGC-JRF (NTA Ref. No.: 201610135853), New Delhi, India, and the third author was partially supported by the JSPS KAKENHI (JP22K03363).

摘要/Abstract

摘要： In this paper, we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball $B_X$ of a complex Banach space $X$ into $\mathbb{C}$. As applications, we will establish refined Bohr inequalities of functional type or of norm type for holomorphic mappings with lacunary series on the unit ball $B_X$ with values in higher dimensional spaces. Next, we obtain the Bohr-Rogosinski inequality for the class of holomorphic functions on $B_X.$ In addition, we establish an improved version of the Bohr inequality for holomorphic functions on $B_X$. All the results are proved to be sharp.

关键词: Banach spaces, Bohr inequality, Bohr-Rogosinski inequality, homogeneous polynomial expansion, Lacunary series

Abstract: In this paper, we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball $B_X$ of a complex Banach space $X$ into $\mathbb{C}$. As applications, we will establish refined Bohr inequalities of functional type or of norm type for holomorphic mappings with lacunary series on the unit ball $B_X$ with values in higher dimensional spaces. Next, we obtain the Bohr-Rogosinski inequality for the class of holomorphic functions on $B_X.$ In addition, we establish an improved version of the Bohr inequality for holomorphic functions on $B_X$. All the results are proved to be sharp.

Key words: Banach spaces, Bohr inequality, Bohr-Rogosinski inequality, homogeneous polynomial expansion, Lacunary series

中图分类号:

32A05

Molla Basir AHAMED¹, Sabir AHAMMED¹, Hidetaka HAMADA^2,*. REFINED BOHR INEQUALITIES AND A REFINED BOHR-ROGOSINSKI INEQUALITY ON COMPLEX BANACH SPACES[J]. 数学物理学报(英文版), 2026, 46(1): 19-38.

Molla Basir AHAMED¹, Sabir AHAMMED¹, Hidetaka HAMADA^2,*. REFINED BOHR INEQUALITIES AND A REFINED BOHR-ROGOSINSKI INEQUALITY ON COMPLEX BANACH SPACES[J]. Acta mathematica scientia,Series B, 2026, 46(1): 19-38.

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REFINED BOHR INEQUALITIES AND A REFINED BOHR-ROGOSINSKI INEQUALITY ON COMPLEX BANACH SPACES

REFINED BOHR INEQUALITIES AND A REFINED BOHR-ROGOSINSKI INEQUALITY ON COMPLEX BANACH SPACES

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