圈上Moebius测度的Sobolev不等式
SOBOLEV INEQUALITIES FOR MOEBIUS MEASURES ON THE UNIT CIRCLE

本文考虑单位圈上的Moebius测度的问题.利用文献[1]和[2]中的方法，把圈上的Moebius测度的估计转化为对一维扩散过程的相关估计上，得到了单位圈上的Moebius测度的Poincaré不等式，对数Sobolev不等式和Sobolev不等式的最佳常数的双边估计.
In this paper, we consider Moebius probability on the unit circle. By using the method in[1] and[2], we transfer the estimates on Moebius probability onto one-dimensional diffusion, and obtain two-sided estimates on optimal Poincaré constant, logarithmic Sobolev constant and Sobolev constant for Moebius measures on the unit circle