Beurling-Ahlfors扩张的伸张函数与ID-同胚  

Dilatation Function of Beurling-Ahlfors Extension and ID-Homeomorphism

作　　者：郑学良[1] 

机构地区：[1]上海交通大学应用数学系

出　　处：《数学学报（中文版）》2002年第5期1035-1040,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(19531060);浙江省教育厅自然科学基金(20010154);台州学院自然科学基金资助项目

摘　　要：本文研究实轴上同胚在上半平面的扩张.利用拟对称函数ρ对伸张函数D作了较精细的估计.同时借助于诱导的边界函数对D、ρ在边界附近的性质作了进一步刻划.作为应用,我们分别给出上半平面存在ID-同胚扩张和IID-同胚扩张的充分条件.In this paper, we study the extensions on the upper half plane of the homeo-morphisms on the real axis.Using the quasisymmetric function, we get a relatively fine estimate of the dilatation function. In the meantime, we give a further characterization on D and p near the boundary by an induced boundary function. As applications, sufficient conditions of the existence of ID homeomorphism and IID homeomorphism are respectively presented.

关 键 词：BEURLING-AHLFORS扩张 伸张函数 ID-同胚 拟对称函数 边界函数 

分 类 号：O174.51[理学—数学]