Asymptotic value of the multidimensional Bohr radius

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.