圈上Moebius测度的Sobolev不等式（英文）  

SOBOLEV INEQUALITIES FOR MOEBIUS MEASURES ON THE UNIT CIRCLE

作　　者：雷良贞 马宇韬 薛丹丹 LEI Liang-zhen;MA Yu-tao;XUE Dan-dan(School of Mathematical Sciences,Capital Normal Univeristy,Beijing 100048,China;School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China;The High School A±liated to Minzu University of China,Beijing 100081,China)

机构地区：[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

出　　处：《数学杂志》2018年第5期813-821,共9页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11471222;11431014; 11371283; 11571043);985 Projects

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Poincar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 dif-fusion,and obtain two-sided estimates on optimal Poincare constant,logarithmic Sobolev constant and Sobolev constant for Moebius measures on the unit circle.

关 键 词：Moebius测度 SOBOLEV不等式 POINCARE不等式 对数SOBOLEV不等式 

分 类 号：O122.3[理学—数学]