关于O_(ⅢКИН)的正规定则

On Oshkin's Normal Criterion

本文建立了一个基本不等式,用一个密指量N_(1-1))(r,1/(f＇f-1))便界囿了于|z|<R(0<R≤+∞)内全纯的函数f(z)的特征函数T(r,f),其中l为一大于等于9的正整数。作为它的应用之一,我们证明了一个正规定则:设F为区域D内的全纯函数族。若F中每个函数f(z)满足性质:f＇(z)f(z)-1在D内零点的重级大于等于9,则F在D内正规,它是正规定则的改进。

A fundamental inequality is established, in which the Nevan-linna characteristic of a holomorphic function is bounded merely by the counting function of distinct l-points of the product of the function under consideration and its derivative, whose multiples are equal to or greater than 9. As one application of this inepuality, a normal criterion is proved. Suppose that F is a family of holomorphic functions in region D. If every function in F stisfies the property that the multiples of 1-points of the product of the function under consideration and its derivative in D are equal to or greater than 9, then F is normal in D, which is an improvement on Oshkin's criterion.