A Criterion of Normality Based on a Single Holomorphic Function

作     者：Xiao Jun LIU Shahar NEVO 

作者机构：Department of Mathematics University of Shanghai for Science and Technology Shanghai 200093 P. R. China Department of Mathematics Bar-Ilan University 52900 Ramat-Gan Israel 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2011年第27卷第1期

页      面：141-154页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：The first author is supported by the Gelbart Research Institute for Mathematical Sciences and by National Natural Science Foundation of China (Grant No. 10671067) the second author is supported by the Israel Science Foundation (Grant No. 395107) 

主　　题：Normal family holomorphic functions zero points 

摘      要：Let F be a family of functions holomorphic on a domain D C C. Let k ≥ 2 be an integer and let h be a holomorphic function on D, all of whose zeros have multiplicity at most k- 1, such that h（z） has no common zeros with any f∈F. Assume also that the following two conditions hold for every f ∈F ：（a） f（z） = 0 == f （z） = h（z）; and （b） y（z） = h（z） == ｜f（k）（z）｜ ≤ c, where c is a *** F is normal on D.