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

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.