| 摘要: |
| 本文主要研究环上的含参变量h的Boltzmann测度μh的对数Sobolev不等式.通过降维方法以及对该不等式最佳常数CLS（μh）的估计，证明了该测度关于h满足一致的对数Sobolev不等式，且对数Sobolev最佳常数CLS（μh）在h > 0时是具有常数阶的.结合已有的结果，再次佐证对数Sobolev不等式严格强于Talagrand传输不等式以及Poincaré不等式. |
| 关键词: Boltzmann测度 对数Sobolev不等式 传输不等式 Poincaré不等式 |
| DOI： |
| 分类号:O177 |
| 基金项目:国家自然科学基金（NSFC11371283，11671076，11871382）. |
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| LOGARITHMIC SOBOLEV INEQUALITY ON BOLTZMANN MEASURES WITH PARAMETER ON CIRCLES |
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CHENG Xin1, MAO Run2, ZHANG Zheng-liang1
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1.Department of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;2.Chongqing No.8 Secondary School, Chongqing 401120, China
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| Abstract: |
| In this paper, we mainly study logarithmic Sobolev inequality on Boltzmann Measures with parameter h > 0 on circles. By the method of dimension-reduction and estimating the Log-Sobolev optimal constant, denoted by CLS(μh), we proved that the family of measures satisfy the uniform logarithmic Sobolev inequality in h and the optimal constant CLS(μh) has a constant order in h, which, together with the known results, enhances the claim that logarithmic Sobolev inequality is strictly stronger than Talagrand's transportation and Poincaré inequalities. |
| Key words: Boltzmann measure logarithmic Sobolev inequality transportation inequality Poincaré inequality |
