亚纯函数微分多项式的一个正规定则

证明了下面两个定理：（1）设n，k≥2为正整数，a为有穷非零复数，F为区域D上的亚纯函数族，F中任一函数的零点重级至少为k．vf，g∈F，fLn（f）与gLn（g）IM分担a．则F在D上正规，其中L（f）为f（k）＋a1f^（k-1）＋…＋akf，这里a1，…，ak为常数．（2）设n，k为正整数，且n≥2，a为有穷非零复数，F为区域D上的亚纯函数族，F中任一函数的零点重级至少为k，且fLn（f（z））=a能够推出｜f^（k）（z）｜≤A，其中A为正数，则F在区域D上正规．

A Normality Criterion for Meromorphic Functions with One of Its Differential Polynomials

In this paper we obtain the following results： 1. Take positive integers n, k ≥2. Let F be a family of meromorphic functions defined on a domain D in the complex plane, such that each f∈F has only zeros of multiplicity at least k. For each pair f,g in F, fLn（f） and gLn（g） share a non-zero complex value a ignoring multiplicity. Then F is normal on D, where L（f） is defined f（k） ＋ alf（k-1） ＋ ... ＋ akf, in which al,…,ak are constants. 2.Take positive integers n and k with n≥2 and take a non-zero complex number a. Let F be a family of meromorphic functions in the plane domain D such that each f∈F has only zeros of multiplicity at least k. For each element f of F,if fLn（f（z）） = a implies If（k）（z）≤A for a positive number A, then F is normal in D.