Generalization of Lohwater-Pommerenke's Theorem

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}.