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圈上Moebius测度的Sobolev不等式
雷良贞¹, 马宇韬², 薛丹丹³
1.首都师范大学数学科学学院, 北京 100048;2.北京师范大学数学科学学院, 北京 100875;3.中央民族大学附属中学, 北京 100081

摘要:

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.

关键词: Moebius测度 Sobolev不等式 Poincaré不等式对数Sobolev不等式

DOI：

分类号:O122.3

基金项目:Supported by National Natural Science Foundation of China (11471222; 11431014; 11371283; 11571043) and 985 Projects.

SOBOLEV INEQUALITIES FOR MOEBIUS MEASURES ON THE UNIT CIRCLE

LEI Liang-zhen¹, MA Yu-tao², XUE Dan-dan³

1.School of Mathematical Sciences, Capital Normal Univeristy, Beijing 100048, China;2.School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;3.The High School Affiliated to Minzu University of China, Beijing 100081, China

Abstract:

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.

Key words: Moebius measures Sobolev inequalities Poincaré inequalities logarithmic Sobolev inequalities