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| 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. |
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| SOBOLEV INEQUALITIES FOR MOEBIUS MEASURES ON THE UNIT CIRCLE |
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LEI Liang-zhen,MA Yu-tao,XUE Dan-dan
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| 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 |
