On Dominating Sets for Nevanlinna Class (I)

Abstract

In this article we prove that a subset $E$ of the open unit disc $U$ is a dominating set for the subclass $N^+$ of the Nevanlinna class $N$ if and only if $E$ is nontangentially dense. When $E$ is a compact subset of $U$, we also give a complete characterization of $E$ to be a dominating set for the subclass $N^-$. Here $N^-$ denotes the proper subclass of $N$ that consists of all of the reciprocal of the singular inner functions.