摘要
对于实轴上满足M条件的自同胚映射h(x),利用一系列积分不等式的精细估计,将相应问题转化为定义在一个凸五边形约束域G上伸张函数f(ξ,η)的估计式;然后根据f(ξ,η)的凸性和其在区域G 5个顶点上函数值的直接计算,从而得到了Beurling-A h lfors扩张映射φ(z)的伸张函数D的最优值估计:D≤2M.本文的证明不同于Lehtinen传统方法.
Let h (x) be a homeomorphism of real axis R onto itself,which satisfies the M-conditions. In terms of relatively fine estimates of integral inequalities,this paper transforms the corresponding problems into the estimates of a dilation function f(ξ,η) defined on a region of convex pentagon. According to the convexity of f(ξ,η) and a direct computation of the values of f(ξ,η) at five vertexes of G,it is shown that dilatation function D(z) of Beurling-Ahlfors' extension mapping φ(z) of h(x) is of optimal estimates: D≤ 2M. This new method is different from Lehtinen's.
出处
《上海交通大学学报》
EI
CAS
CSCD
北大核心
2005年第10期1737-1740,共4页
Journal of Shanghai Jiaotong University
基金
国家自然科学基金资助项目(10271077)
浙江省教育厅自然科学基金(20030768)