一阶连续模形式下的Kellogg定理

Kellogg Theorem in Form of 1-order Module of Continuity

从单位圆到以光滑 Jordan曲线为边界的单连通区域的共形映射 ,其边界的光滑性有经典的 Kel-logg定理及其推广的 Warschawski定理。以连续模为工具对原结果进行了深入的讨论 ,得到了更为一般的结果。

By using the tools of the module of continuity, this paper discusses the conformal mapping from a unit circle onto a simply connected region enclosed by a smooth Jordan curve, the smooth properties of its border are illustrated by the Kellogg's theorem and its extended Warschawski's theorem. This paper concentrates on making deeper discussions on the original results of these theorems and obtains more general results.