涉及无零点的亚纯函数的正规定则

Normality criteria of zero-free meromorphic functions

设F为区域D内一族非零亚纯函数且所有的极点是二重,k是正整数.h(z)(■0,∞)是区域D■C内亚纯函数且所有极点是简单极点.若对于■f∈F,L(f)-h(z)至多有k个不同零点(不计重数),则F在区域D上正规.

Let F be a family of non-zero meromorphic functions in region D,and all polesk are heavy poles,k is a positive integer.h(z)(■0,∞)is a homomorphic function in region D,and all poles are simple poles.If for ■f∈F,(L(f))-h(z),has at most k different zeros(regardless of multiplicity),then F is normal in region D.