Beurling-Ahlfors扩张的伸张函数的估计

数学季刊 ›› 2005, Vol. 20 ›› Issue (1): 65-71.

Beurling-Ahlfors扩张的伸张函数的估计

Department of Mathematics, Taizhou University, Linhai 317000, China; College of Mathematics and Information Sciences, Henan University, Kaifeng 475001, China

收稿日期:2004-09-18 出版日期:2005-03-30 发布日期:2024-02-26
作者简介:ZHENG Xue-liang(1954-),male,native of Linhai,Zhejiang,a professor of Taizhou University, engages in complex analysis.
基金资助:
Supported by the National Natural Science Foundation of China(10271077) Supported by the Educational Department of Zhejiang Province Natural Science Project(20030768)；

Estimates of the Dilatation Function of Beurling-Ahlfors Extension

Department of Mathematics, Taizhou University, Linhai 317000, China; College of Mathematics and Information Sciences, Henan University, Kaifeng 475001, China

Received:2004-09-18 Online:2005-03-30 Published:2024-02-26
About author:ZHENG Xue-liang(1954-),male,native of Linhai,Zhejiang,a professor of Taizhou University, engages in complex analysis.
Supported by:
Supported by the National Natural Science Foundation of China(10271077) Supported by the Educational Department of Zhejiang Province Natural Science Project(20030768)；

摘要/Abstract

摘要： In this paper, we prove that the control function of the dilatation function of Beurling-Ahlfors extension is convex. Using the quasi-symmetric function ρ, we get a relatively sharp estimate of the dilatation function: D(x,y)≤17/32 (ρ(x, y) + 1) (ρ(x + y/2, y/2) +ρ(x - y/2, y/2) +2) , which improves the results before. We also show that the above result is asymptotically precise.

关键词: Beurling-Ahlfors , , extension;quasi-symmetric , , function;dilatation , , function;con-
trol , function

Abstract: In this paper, we prove that the control function of the dilatation function of Beurling-Ahlfors extension is convex. Using the quasi-symmetric function ρ, we get a relatively sharp estimate of the dilatation function: D(x,y)≤17/32 (ρ(x, y) + 1) (ρ(x + y/2, y/2) +ρ(x - y/2, y/2) +2) , which improves the results before. We also show that the above result is asymptotically precise.

Key words: Beurling-Ahlfors , , extension;quasi-symmetric , , function;dilatation , , function;con-
trol , function

中图分类号:

O174.51

郑学良, 王建平. Beurling-Ahlfors扩张的伸张函数的估计[J]. 数学季刊, 2005, 20(1): 65-71.

ZHENG Xue-liang, WANG Jian-ping . Estimates of the Dilatation Function of Beurling-Ahlfors Extension[J]. Chinese Quarterly Journal of Mathematics, 2005, 20(1): 65-71.

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