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 functio...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.展开更多
基金Supported by the National Natural Science Foundation of China(10271077)Supported by the Educational Department of Zhejiang Province Natural Science Project(20030768)
文摘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.
