On the dilatation estimates for Beurling-Ahlfors quasiconformal extension
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- Proc. Amer. Math. Soc. 100 (1987), 655-660 Request permission
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 $\rho$.References
- A. Beurling and L. Ahlfors, The boundary correspondence under quasiconformal mappings, Acta Math. 96 (1956), 125–142. MR 86869, DOI 10.1007/BF02392360
- Terence J. Reed, Quasiconformal mappings with given boundary values, Duke Math. J. 33 (1966), 459–464. MR 196074
- Zhong Li, On the Beurling-Ahlfors extension, Acta Math. Sinica 26 (1983), no. 3, 279–290 (Chinese). MR 721679
- Lars V. Ahlfors, Lectures on quasiconformal mappings, Van Nostrand Mathematical Studies, No. 10, D. Van Nostrand Co., Inc., Toronto, Ont.-New York-London, 1966. Manuscript prepared with the assistance of Clifford J. Earle, Jr. MR 0200442
- Matti Lehtinen, The dilatation of Beurling-Ahlfors extensions of quasisymmetric functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 8 (1983), no. 1, 187–191. MR 698846, DOI 10.5186/aasfm.1983.0817
Additional Information
- © Copyright 1987 American Mathematical Society
- 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