| Beurling-Ahlfors扩张的伸张函数的估计 |
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| 作者姓名： | ZHENG Xue-liang WANG Jian-ping |
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| 作者单位： | Department of Mathematics，Taizhou University，Linhai 317000，China; College of Mathematics and Information Sciences，Henan University，Kaifeng 475001，China |
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| 基金项目： | Supported by the National Natural Science Foundation of China(10271077)
Supported by the Educational Department of Zhejiang Province Natural Science Project(20030768) |
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| 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.
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| 关 键 词： | 单项变换函数 Beurling-Ahlfors扩张 准对称方程 控制函数 复平面 |
Estimates of the Dilatation Function of Beurling-Ahlfors Extension |
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| 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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| Authors: | ZHENG Xue-liang WANG Jian-ping |
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| Abstract: | |
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| Keywords: | Beurling-Ahlfors extension quasi-symmetric function dilatation function control function |
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