关于两类Shimizu-Ahlfors特征函数

ON TWO SHIMIZU-AHLFORS CHARACTERISTIC FUNCTIONS

本文研究了单出圆盘内亚纯函数 f 的两类 p 级 Shimizu-Ahlfors 特征函数,对影响这两类特征函数的几个参变量逐一进行了探讨。分别得到了 f 属于某些重要的函数空间如正规函数族,有界特征的函数族,一致有界特征的函数族等的充分必要条件.

In this paper we study two Shimizu-Ahlfors charcteristic functions of f meromorphic in the disk D and consider the parameters on which the characteristic functions depend.We give some necessary and sufficient conditions for a meromorphic f to belong to certain important function spaces in terms of the Shimizu-Ahlfors charcteristic functions.