分担多项式的全纯函数的正规族

Normal families of holomorphic functions shared polynomial

运用Zalcman引理,证明了设F为区域D内的一个全纯函数族,k∈N+(≥2),P(z)是一个多项式,且(P(z))<k,若f∈F,f和f′CM分担P(z),且当f(z)=P(z),z∈D时,有|f(k)|≤K,则F在D上是正规的.此结论推广了徐炎,刘志宏所证明的关于正规性的一些结果.

Using the Zalcman lemma, it is proved that let F be a family of holomorphic functions in a domain D,k（≥2） be a positive integer and let P（z） be a polynomial and Э（P （z）） 〈 k. If eachf∈F,K be a positive inte-ger, when f（z） = P （z） ,z ∈ D, then ｜f（k）｜≤ K, where f and f shared P （z）, then F is normal in D. Some normality criterions proved by XU Yan and LIU Zhi-hong are extended and improved by this result.