A maximal version of the multidimensional Khinchin-Ostrovskii theorem and its applications (Q2455302)

Let \(G\) be either the unit ball in \(\mathbb C^n\) or the unit polydisk in \(\mathbb C^n.\) The main result of this paper is the multidimensional variant of the Khinchin-Ostrovskii theorem for the domain \(G\) (Theorem 1). Later on the authors obtain a compactness criterion for subsets of a certain space of holomorphic functions on \(G\) using Theorem 1.