Warschawski定理的推广

Some Extension on the Warschawski Theorem

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Kellogg定理及其推广的 Warschawski定理 ,本文以连续模、P次平均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 and modulus of continuity in P-mean, this paper discusses the conformal mapping from a unit circle onto a simply connected region enclosed by a smooth Jordan curve, about the smooth property of the boarder of which there are 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.