发表机构
Amity School of Applied Sciences, Amity University Mumbai; Department of Mathematics, Raiganj University（孟买阿密特大学应用科学学院; 拉根杰大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在Banach空间和JB*-三元组上建立了涉及Schwarz映射的精细Bohr不等式，推广了已有结果并获得了改进的Bohr半径。
AI 中文摘要
本文研究了定义在复Banach空间单位球 \\( B_X \\) 上的全纯映射的涉及Schwarz映射的精细Bohr型不等式。我们首先建立了标量值全纯映射 \\( F: B_X \to \mathbb{U} \\) 的精细Bohr不等式。然后，我们将一些结果推广到涉及Schwarz映射的向量值全纯映射，形式为 \\( F: B_X \to \overline{\mathbb{U}}^{\\,n} \\)（\\( n \ge 2 \\)），在适当的范数条件下获得了改进的Bohr半径。此外，我们研究了值域包含在JB$^*$-三元组单位球闭包中的全纯映射的涉及Schwarz映射的Bohr半径。我们的结果推广了Jia等人\\(\cite{JLP}\\)、Liu等人\\(\cite{LLP2021}\\)和Liu等人\\(\cite{LSX2018}\\)的结果。
英文摘要
In this paper, we investigate refined Bohr-type inequalities involving Schwarz mappings for holomorphic mappings defined on the unit ball \( B_X \) of a complex Banach space. We first establish refined Bohr inequalities for scalar-valued holomorphic mappings \( F : B_X \to \mathbb{U} \). We then extend some results to vector-valued holomorphic mappings involving Schwarz mappings of the form \( F : B_X \to \overline{\mathbb{U}}^{\,n} \), \( n \ge 2 \), where improved Bohr radii are obtained under suitable norm conditions. Furthermore, we study the Bohr radius involving Schwarz mappings for holomorphic mappings whose ranges are contained in the closure of the unit ball of a JB$^*$-triple. Our results generalize the results of Jia \textit{et al.} \cite{JLP}, Liu \textit{et al.} \cite{LLP2021} and Liu \textit{et al.} \cite{LSX2018}.
