Arithmetic Bohr radius for the Minkowski space

Abstract

The main aim of this paper is to study the arithmetic Bohr radius for holomorphic functions defined on a Reinhardt domain in ℂ n {\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 ℓ q n {\ell^{n}_{q}} , 1 ≤ q ≤ ∞ {1\leq q\leq\infty} . Further, we determine the exact value of a Bohr radius in terms of arithmetic Bohr radius.