Asymptotic value of the multidimensional Bohr radius

TL;DR

This paper precisely determines the asymptotic behavior of the Bohr radius for holomorphic functions on high-dimensional $ ext{ell}_p^n$ spaces and explores sharp bounds for various function classes mapping into specific complex domains.

Contribution

It provides the exact asymptotic value of the multidimensional Bohr radius and investigates sharp bounds for different classes of holomorphic functions.

Findings

Exact asymptotic value of the Bohr radius for $ ext{ell}_p^n$ spaces.

Sharp Bohr radius bounds for functions into specific complex domains.

Analysis of four categories of holomorphic functions with different target domains.

Abstract

This article determines the exact asymptotic value of the Bohr radii and the arithmetic Bohr radii for the holomorphic functions defined on the unit ball of the $\ell_p^n$ space and having values in the simply connected domain of $\mathbb{C}$. Moreover, we investigate sharp Bohr radius for four distinct categories of holomorphic functions. These functions map the bounded balanced domain $G$ of a complex Banach space $X$ into the following domains: the right half-plane, the slit domain, the punctured unit disk, and the exterior of the closed unit disk.