关于Beurling和Ahlfors的一个定理

赖万才

数学学报 ›› 1979, Vol. 22 ›› Issue (2) : 178-184.

数学学报 ›› 1979, Vol. 22 ›› Issue (2) : 178-184. DOI: 10.12386/A1979sxxb0015
论文

关于Beurling和Ahlfors的一个定理

    赖万才
作者信息 +

ON A THEOREM OF BEURLING AND AHLFORS

Author information +
文章历史 +

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 :

引用本文

导出引用
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

Accesses

Citation

Detail

段落导航
相关文章

/