论文标题
Plessner定理的强烈形式
A strong form of Plessner's theorem
论文作者
论文摘要
令$ f $为单位光盘上的全体形态，甚至是meromormorphic的功能。然后，Plessner定理说，对于几乎每个边界点$ζ$，（i）$ f $在$ζ$时具有有限的非目标限制，或（ii）任何stolz angle $ s $的图像$ f（s）$ s $ at $ζ$在复杂的平面中是密集的。本文表明，陈述（ii）可以用更强的断言代替。这种新定理及其在半个空间上的谐波功能的类似物也增强了Spencer，Stein和Carleson的经典结果。
Let $f$ be a holomorphic, or even meromorphic, function on the unit disc. Plessner's theorem then says that, for almost every boundary point $ζ$, either (i) $f$ has a finite nontangential limit at $ζ$, or (ii) the image $f(S)$ of any Stolz angle $S$ at $ζ$ is dense in the complex plane. This paper shows that statement (ii) can be replaced by a much stronger assertion. This new theorem and its analogue for harmonic functions on halfspaces also strengthen classical results of Spencer, Stein and Carleson.
