Multidimensional Bohr radii for holomorphic functions with values in complex Banach spaces

TL;DR

This paper investigates multidimensional Bohr radii for vector-valued holomorphic functions in complex Banach spaces, providing asymptotic estimates and exact values for mixed Bohr radii in specific domains.

Contribution

It offers new asymptotic estimates and exact calculations for classical and mixed Bohr radii for vector-valued holomorphic functions in complex Banach spaces.

Findings

Asymptotic estimates of classical Bohr radius in $ ext{ell}^n_q$ spaces.

Exact value of mixed arithmetic Bohr radius.

Analysis of Bohr radii in complete Reinhardt domains.

Abstract

The main aim of this paper is to study multidimensional Bohr radii for holomorphic functions defined in complete Reinhardt domains in $\mathbb{C}^n$ with values in complex Banach spaces. More specifically, for holomorphic functions with values in arbitrary complex Banach spaces, we explore the asymptotic estimates of the classical Bohr radius and arithmetic Bohr radius in the unit ball of $\ell^n_q$ $(1\leq q\leq \infty)$ spaces. Further, we study a mixed version of Bohr radii for vector-valued holomorphic functions and as a consequence we obtain the exact value of mixed arithmetic Bohr radius.