Existence domains of holomorphic functions of restricted growth

Abstract:

The paper presents a large class of domains $G$ of holomorphy in ${{\mathbf {C}}^n}$ such that, for any $N > 0$, there exists a nonextendable holomorphic function $f$ on $G$ with $|f|\delta _G^N$ bounded where ${\delta _G}(z): = \min ({(1 + |z{|^2})^{ - 1 / 2}}, \operatorname {dist} (z, \partial G))$. Any fat Reinhardt domain of holomorphy belongs to this class. On the other hand we characterize those Reinhardt domains of holomorphy which are existence domains of bounded holomorphic functions.