涉及微分多项式的亚纯函数的正规族

设F是区域D内的一族亚纯函数,k,m,q是正整数,P(ω)=ωq+aq-1(z)ωq-1+…+a1(z)ω是一多项式,H(f,f′,…,f(k))是满足γH*0的微分多项式,a(z),b(z),c(z)是区域D内的解析函数,且a(z)≠b(z),c(z)≠0.若对于任意的f∈F,f的零点的重数至少是k+1,且有(1)P(f(k)(z))+H(f,f′,…,f(k))=a(z)时,f(z)=0;(2)P(f(k)(z))+H(f,f′,…,f(k))=b(z)时,f(z)=c(z),则F在D内正规.

On Normal Families of Meromorphic Functions with Differential Polynomial

Let F be a family of meromorphic function on D, k, m, q be positive numbers,P(ω)=ω~q+a_(q-1) (z)ω~(q+1)+…+a_1(z)ω is a polynomial. Let H(f,f',…,f(~((k))) be a differential polynomial that satisfies r_H~*>0,a(z) ,b(z),c(z) be some analytic functions in D and a(z)≠b(z), c(z)≠0. If, for every function f∈ F, the zeros of f have multiplicity at least k+1, and (1) Let P(f~((k))(z)+H(f,f',…,f~((k)))=a(z),then f(z)=0;(2)Let P(f~((k))(z)+H(f,f',…,f~((k)))=b(z),then f(z)=c(z).Then F is normal in D.