关于有界全纯函数在边界附近的某些性质

<正> 在1]中 H.G.Eggleston 曾经证明了如下一个很有用的定理.设 f(z)是区域 D 内的有界全纯函数并 z_0为 D 的某一界点,z_0可为∞,但 D 至少人含有一有限还点为其界点.让 L 是一弧而以 z_0为其一端点且其他各点全属 D 内.若

CONCERNING THE PROPERTIES OF BOUNDED REGULAR FUNCTION IN THE NEARLY BOUNDARY

In this paper,we have proved a theorem which extend the Tauberian lemmaconsidered by Rogosinsky et Eggleston and we have obtained several corolla-ries:Theorem 1.Let f(z)be a bounded regular function with finite number ofzeros in domain D, and z_o be a point on the frontier of D.z_o may be the pointat infinity,but in any case the frontier of D must contain at least one finitepoint.Let S(?)D be a set of points,z_o is one of its limit points,for z∈D,letd(z)be the distance of z from the frontier of D.(?)Corollary 1.With the same hypotheses as in Theorem 1,let G_x be a subsetof D which consists of(i)all the points z_1 of S;(ii)all the points z of D whichsatisfy(?)for some z_1 of S,where x is a fixed number,0