English

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 FF from the unit ball BX\mathbb{B}_X of a complex Banach space XX into the closure of the unit polydisc Dm\mathbb{D}^m within the space Cm\mathbb{C}^m. 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 FνF\circ \nu, where ν\nu is a Schwarz mapping with a zero of order kk 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}
}