涉及重级零点的亚纯函数的拟正规定则

Quasinormal Criterion of Meromorphic Functions with Multiple Zeros

设F为区域D内的只有重级零点的亚纯函数族,H(z)为区域D内的非常数亚纯函数,且存在v∈N,使得对于任意的a∈C,n(D,1/H(z)-a)≤v.如果对于任意的f∈F,f′(z)≠H′(z),那么F在区域D内v阶拟正规.

Let F be a family of meromorphic functions in D, whose zeros are all multiple Let H（z） be a nonconstant meromorphic function in D, and there exists a V ∈N, such that for each a ∈C, n（D, ~1/H（z）-a）≤V,If for each f∈F, f′（z） ≠H＇（z）, then F is quasinormal of order v in D.