几个拟共形扩张条件和万有Teichmüller空间的表示定理

Some conditions of the qusiconformal extension and representative theorems of the universal Teichmüller space

记扩充复平面为 C,z=x+iy,G={|z|【1},A=C\G,∑表示由△内单叶解析函数g（z）=z+b0+sum from n=1 to n bnz-n,|z|】1 （1）的类,∑k 表示∑内有由⊿到 G 内的 K 一拟共形扩张的子类。全体能拟共形扩张的解析函数所组成的空间可看作万有 Teichmüller 空间。单叶函数存在拟共形扩张的是一个重要的研究课题,L.Ahlfors 等曾进行过研究。本文从不同角度,建立函数存在拟共形扩张的几个充要条件和充分条件。

Let G={|z|<1),Δ=C\G,Σ be a class of univalent analytic functions g（z）=z+sum from n=0 to ∞bnz-n,z∈Δ,and Σk be a subclass of Σ,its element g∈Σ has a k-quasiconformal extension to G.We establish some sufficient and necessary conditions of g∈Σk,they are also the representative Theorems of The Univ- ersal Teichmüller Space.Morever,we also give some estimates of coefficients for Σk.