分担全纯函数的亚纯函数的正规族（英文）

Normal Families of Meromorphic Functions and Shared Holomorphic Functions

主要研究了亚纯函数分担全纯函数的正规族问题,证明了:如果F是区域D上的亚纯函数族,且满足L[f]=a0f'+a1f(a0≠0),a,b,c,d为D上的4个全纯函数。如果对任意的f∈F,满足a(z)≠d(z),b(z)+a1(z)a(z)+a0(z)a'(z)≠2c(z),c(z)-a0(z)a'(z)-a1(z)a(z)≠0,f(z)=a(z)L[f](z)=b(z)且L[f](z)=c(z)f(z)=d(z),则F在D正规。

In this paper, we discuss the normality criterion concerning shared holomorphic functions, and prove that if ￡ bea family of meromorphic functions in a domain D,L[f]=a0f＇＋a1f（a0≠O）, and a,b, c,d be four holomorphic functions in D. For eacha f∈￡,if a（z）≠d（z）,b（z）＋a1（z）a（z）＋a0（z）a＇（z）≠2c（z）,c（z）-a0（z）a＇（z）一a1（z）a（z）≠0,f（z）=a（z）→L[f]（z）一b（z）and L[f]（z）=c（z）→f（z）=d（z）, then ￡is normal in D.