BEURLING-AHLFORS扩张的伸张函数在边界附近的性质

Properties of the Dilatation Function Near the Boundary of BEURLING-AHLFORS Extension

研究Beurling-Ahlfors扩张的伸张函数在实轴附近的性质。定义了边界函数,证明了g(x)几乎处处有界,且‖g(x)‖_∞≤8。

In this paper, we study the properties of the dilatation function near the boundary of the Beurling - Ahlforsextension. The concept of boundary function is defined. We prove the following result: ‖g(x)‖_∞≤8a. e.