Arithmetic Bohr radius for the Minkowski space

The main aim of this paper is to study the arithmetic Bohr radius for holomophic functions defined on a Reinhardt domain in ${\mathbb{C}}^n$ with positive real part. The present investigation is motivated by the work of Lev Aizenberg [Proc. Amer. Math. Soc. 128 (2000), 2611–2619]. A part of our study in the present paper includes a connection between the classical Bohr radius and the arithmetic Bohr radius of unit ball in the Minkowski space ${\mathrm{\ell }}_q^n,1\le q\le \mathrm{\infty }$. Further, we determine the exact value of a Bohr radius in terms of arithmetric Bohr radius.