圆内亚纯函数的特征函数

THE CHARACTERISTIC FUNCTION OF MEROMORPHIC FUNCTION IN CIRCLE

假设f(z)是单位圆的半纯函数,且f(0)≠0,∞。那么有如下结论: (ⅰ)对0<r<R<1,有: T(r,f')≤2T(r,f)+3l_n^(R-r)^(-1)+4l_n^T(R,f)+C (ⅱ)对任给ε>0,和任给的实函数h(r)≥1,存在常数c,满足: T(r,f)≤cA^(1+ε)(r)(1-r)^(-1+ε)·T(R,f') 其中R=[1+rh(r)][1+h(r)]^(-1)

Let f(z) be a meromorphic function in | z | < 1 , and f ( 0 )≠0 , 888888888. Then (i)for 0<r<R<l, T(r,f')≤2T(r,f)+3ln+1/R-r+4ln+T(R,f) +c ( ii ) for any ∞>0, and any real function h ( r )≥1 ,there exists constant C , such that where R=1+rh(r)/1+h(r).