Refined Bohr Inequalities and Bohr Radii Involving Schwarz Mappings for Holomorphic Functions in Banach Spaces and JB*-Triples
Year: 2026
Type: preprint
Abstract: 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}.
Source: arXiv (Cornell University)
Authors: Sarkar, Nabadwip, Das, Pradip
Institutions: Raiganj University, Amity University Mumbai
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G489438624
OpenAlex ID: W7220439091