全纯函数的一个正规族

摘要

设F为单位圆盘△上的一个全纯函数族,M,N为两个正实数.如果对于任意的f∈F,f的零点重级≥m,且f(z)=0(=) |f(m)(z)|≤M,f(m)(z)=1(=)|f(z)|≥N,则F在△上正规.%A normality criterion for a family of holomorphic functions was got. Let F be a family of holomorphic functions on the unit disk △, all of whose zeros are of multiplicity at least m; let M, N be two positive numbers; if for any f ∈ F, f(z) = 0 (=) |f(m)(z)| ≤ M, f(m)(z) = 1 (=) |f(z)| ≥ N,then F is normal on △.