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Proceedings of the American Mathematical Society

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On the dilatation estimates for Beurling-Ahlfors quasiconformal extension


Author: De Lin Tan
Journal: Proc. Amer. Math. Soc. 100 (1987), 655-660
MSC: Primary 30C60
DOI: https://doi.org/10.1090/S0002-9939-1987-0894433-0
MathSciNet review: 894433
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Abstract: Let $ \mu (x)$ be a $ \rho $-quasisymmetric function. Then the dilatation $ K(z)$ of Beurling-Ahlfors extension with $ r = 1$ satisfies the inequalitites $ K \leq 2\rho - 7(\rho - 1)/6(\rho + 1)$ and $ K < 2\rho - 2 + O(1/\rho )$ for sufficiently large $ \rho $.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0894433-0
Article copyright: © Copyright 1987 American Mathematical Society