摘要
<正> 1.一个把实轴映成自身的连续的严格增加函数μ叫做ρ拟对称的,1≤ρ<∞,如果对一切x和t≠0成立.Beurling和Ahlfors证明:任何一个给定的ρ拟对称函数μ,必可拓广成上半平面到自身的一个皮拟共形映照,具有
Abstract
A continuous strictly increasing function μ mapping the real line onto itself is called ρ-quasisymmetric, 1 ≤ ρ < ∞, if 1/ρ ≤ μ(x + t) - μ (x)/μ(x)-μ(x-t)≤ ρ(1) for all x and all t ≠ 0. Beurling and Ahlfors first proved that any given ρ-quasisymmetrie funetion μ has an extension to a K-quasiconformal homeomorphismfrom the upper half-plane onto itself with K≤ρ~2.(2) Reed then improved the inequality (2) as follows: K < 8ρ.(3)In the present paper we give a detailed exposition of the computation for the inequality (2) (for [2], such an exposition may be concerned with by Reed because in [3] Lehto and Virtanen obtained K ≤ 8ρ(ρ + 1)~2 only) and prove the following result :
赖万才.
关于Beurling和Ahlfors的一个定理. 数学学报, 1979, 22(2): 178-184 https://doi.org/10.12386/A1979sxxb0015
ON A THEOREM OF BEURLING AND AHLFORS. Acta Mathematica Sinica, Chinese Series, 1979, 22(2): 178-184 https://doi.org/10.12386/A1979sxxb0015
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脚注
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