H_α中函数的从属性

Subordinative of Functions in H_α

设H是单位园盘D={z;|z|<1)中的正则函数族,其中的函数满足f(0)=f’(0)-1=0;用H_0表示H的一个子族.其中的函数具有如下的形式:此处(z)是S中的正则函数.且|(z)|<1.(z∈D)(0)=0.对于f(z)∈H_0.本文主要证明了:若.其中从而把我们在文献[2]中a=1和a=2的结果推广到a≥1的一般情形.

in this paper, the following theorem is obtained. theorem let D={z||z|<1}, u'(z) is regular function in D and |u'(z)|<1 u'(0)=0 z∈D; if f(z)∈H_n, α≥1, then (f(z)/z)-(G(z)/z) Here G(z)={1/α integral from n=0 to (u (1/α)-1) 1/(1-u)^(2/α)du]~α thus we extend the result of literature [2] to gereral condition α≥1.