On multidimensional Bohr radius of finite dimensional Banach spaces

TL;DR

This paper improves the lower bounds of the multidimensional Bohr radius for bounded holomorphic functions on finite-dimensional $ ext{ell}^n_q$-spaces, advancing understanding of these radii in complex Banach spaces.

Contribution

It provides an improved lower estimate for the multidimensional Bohr radius in finite-dimensional $ ext{ell}^n_q$-spaces, refining previous bounds by Defant, Maestre, and Schwarting.

Findings

Enhanced lower bounds for the Bohr radius in $ ext{ell}^n_q$-spaces.

Refined estimates improve understanding of holomorphic functions in Banach spaces.

Advances previous results by providing tighter bounds.

Abstract

In this paper, we improve the lower estimate of multidimensional Bohr radius for unit ball of $\ell^n_q$-spaces ($1\leq q\leq \infty$) for bounded holomorphic functions with values in finite dimensional complex Banach spaces. The new estimate provides the improved lower bound for the Bohr radius which was previously given by Defant, Maestre, and Schwarting [Adv. Math. 231 (2012), 2837--2857].