全纯函数族的一些正规定则

Some Normality Criteria for Families of Holomorphic Functions

设F为区域D内的一族全纯函数,k为正整数,n0,…,nk为k个非负整数,满足n0+…+nk≥2,且存在ni≥1(0≤i≤k-1).若对任意f(z)∈F,f(z)的零点重数≥k,且fn0(z)(f(′z))n1…(f(k)(z))nk≠1,则F在D内正规.

Let be a family of holomorphic functions in a domain D, and no,…, nk be k non-negative integers with no＋…＋nk≥12 and with some ni≥1（0≤i≤k-1）.If for every function f（z）∈ ,the zeros off（z） have multiplicities at least k,and f^n0（z）（f（z））^n1…（f^（k）（z））^nk≠1, then is normal in D.