涉及分担函数的全纯函数的正规族

Normal Families of Holomorphic Functions Involving Shared Holomorphic Functions

主要研究了涉及分担函数的全纯函数的正规定则。雷春林,杨德贵和方明亮等证明了在亚纯函数族中,函数的零点至少为k+1重,且对任意一个函数与其k(≥2)阶导数分担一个全纯函数,则该函数族正规。本文利用Zalcman-Pang方法,证明了全纯函数在k=1的情况。设a(z)(≠0),b(z)(■0)为区域D内的两个全纯函数,F是区域D内的全纯函数族,其若对族中每一个函数f,f的零点均为重级,且f=a(z)■f′=b(z),则F在D内正规。

This paper mainly talks about the normality criterion for a family of holomorphic functions involving shared holomorphic functions.Lei Chunlin,Yang Degui,Fang Mingliang and others have proved that if zero of meromorphic functions is at least k+1 multiple and share a holomorphic function with the derivative of k(≥2),then the function is of normal families.This paper gives a proof of the holomorphic function when k=1 by the method of Zalcman-Pang.Let a(z)(≠0),b(z)(■0) be two holomorphic functions on D,F be a family of holomorphic functions in domain D,all of whose zeros are of multiple,and for each f∈F,f=a(z)■f′=b(z),then F is normal in D.