Bohr inequalities for holomorphic mappings in higher-dimensional complex Banach spaces
Complex Variables
2025-11-25 v1
Abstract
In this paper, we investigates the Bohr phenomenon for holomorphic mappings from the unit ball of a complex Banach space into the closure of the unit polydisc within the space . First, we prove an improved Bohr inequality involving the squared norms of the mapping and its homogeneous expansions. Second, we derive a refined Bohr inequality that incorporates a combination of the coefficient norms and their squares. Finally, we obtain a refined Bohr inequality for compositions , where is a Schwarz mapping with a zero of order at the origin. For each result, we demonstrate that the derived Bohr radius is sharp.
Keywords
Cite
@article{arxiv.2511.18953,
title = {Bohr inequalities for holomorphic mappings in higher-dimensional complex Banach spaces},
author = {Vasudevarao Allu and Raju Biswas and Rajib Mandal},
journal= {arXiv preprint arXiv:2511.18953},
year = {2025}
}