摘要
In this paper, we provefunction of Beurling-Ahlfors extensionthat the control function of the dilatation is convex. Using the quasi-symmetric function p, we get a relatively sharp estimate of the dilatation function: D(x,y) < 17/32 (p(x, y) + 1) (p(x + y/2, y/2) + p(x-y/2, y/2) + 2) , which improves the results before.We also show that the above result is asymptotically precise.
In this paper, we prove that the control function of the dilatation function of Beurling-Ahlfors extension is convex. Using the quasi-symmetric function ρ, we get a relatively sharp estimate of the dilatation function: D(x,y)≤ 17/32 (ρ(x, y) + 1) (ρ(x + y/2, y/2) +ρ(x - y/2, y/2) +2) , which improves the results before. We also show that the above result is asymptotically precise.
基金
Supported by the National Natural Science Foundation of China(10271077)Supported by the Educational Department of Zhejiang Province Natural Science Project(20030768)
