arXiv subjects
Publications and source records attributed to P. V. Dovbush.
In this paper, as an application of Zalcman's lemma in $\mathbb{C}^n$, we give a sufficient condition for normality of holomorphic functions of several complex variables, which generalizes previous known one-dimensional criterion of A.J. Lohwater and Ch. Pommerenke \cite[Theorem 1]{MR0338381}.
The aim of this note is to give a proof of the Schottky theorem in general domains in $\mathbb{C}^n$. The proof is short and works for the cases $n = 1$ and $n > 1$ at the same time.
The aim of this paper is to give some applications of Zalcman's Rescalling Lemma.
The aim of this paper is to give a proof of improving of Zalcman's lemma.
Extension of classical Mandelbrojt's criterion for normality of a family of holomorphic zero-free functions of several complex variables is given. We show that a family of holomorphic functions of several complex variables whose corresponding Levi form are uniformly bounded away from zero is normal.
The aim of the present article is to establish the connection between the existence of the limit along the normal and an admissible limit at a fixed boundary point for holomorphic functions of several complex variables.