Beurling-Ahlfors扩张的伸张函数与ID-同胚

郑学良

数学学报 ›› 2002, Vol. 45 ›› Issue (5) : 1035-104.

PDF(453 KB)
PDF(453 KB)
数学学报 ›› 2002, Vol. 45 ›› Issue (5) : 1035-104. DOI: 10.12386/A2002sxxb0134
论文

Beurling-Ahlfors扩张的伸张函数与ID-同胚

    郑学良
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Dilatation Function of Beurling-Ahlfors Extension and ID-Homeomorphism

    Xue Liang ZHENG
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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.

Abstract

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 / ID-同胚 / 伸张函数 / 边界函数 / 拟对称函数

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郑学良. Beurling-Ahlfors扩张的伸张函数与ID-同胚. 数学学报, 2002, 45(5): 1035-104 https://doi.org/10.12386/A2002sxxb0134
Xue Liang ZHENG. Dilatation Function of Beurling-Ahlfors Extension and ID-Homeomorphism. Acta Mathematica Sinica, Chinese Series, 2002, 45(5): 1035-104 https://doi.org/10.12386/A2002sxxb0134
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