一个涉及亚纯函数的正规定则(英文)

A Normality Criterion of Meromorphic Functions

假设F是区域D■C的亚纯函数族,又设k是一个正整数,a,b(≠a),c(≠a)是3个有限复数且h1,h2,h3是3个正数.若对每个函数f∈F有f(z)=a■|f(k)(z)|≤h1,f(z)=b■f(k)(z)|≤h2,f(k)(z)=c■|f(z)|≥h3,且f所有的零点的重级不小于k,则F在D内正规.

Let F be a family of meromorphic functions in a domain D■C,all of whose zeros are of multiplicity at least k.Let k be a positive integer,and let a,b and c be three finite complex numbers such that a≠b,a≠c and h1,h2,h3 be three positive numbers.If f(z)=a ■|f(k)(z)|≤h1,f(z)=b ■ |f(k)(z)|≤h2,f(k)(z) =c■|f(z)|≥h3 for every f∈F,and all f s zeros are of multiplicity at least k,then F is normal in D.