亚纯函数的正规族

Normal Families of Meromorphic Functions

设为F区域D上亚纯函数簇,k∈Z+(k≥2),m∈Z+,a≠0,b为两有穷复数,c(z)≠0为D上解析函数,f∈F,f′(z)的零点之级≥m,并且f(z)在区域D上的极点总个数(计算重数)至多为m个,f(z)=a f′(z)=b,f(z)=0 0 f′(z)=c(z),f′(z)=c(z)|f(k)(z)|≤h,那么F在区域D内正规.

Let F be a family of meromorphic functions in a domain D, let k ≥2, m be two positive in tegers. Let a ≠0, b be two finite complex numbers; and let c（z） be a function holomorphic in D such that c（z） ≠0 for z ∈ D. If, for every f∈ F, all zeros off（z） have multiplicity ≥m , the number of all poles of f＇（z） in D is at most m andf（z） = a→f（z） = b,f（z） =0→f（z） =c（z）,f＇（z） =c（z）→｜f^（k） （z）｜≤h, then F is normal in D.