环上含参变量的Boltzmann测度的对数Sobolev不等式  

LOGARITHMIC SOBOLEV INEQUALITY ON BOLTZMANN MEASURES WITH PARAMETER ON CIRCLES

作　　者：程新 毛闰 张正良[1] CHENG Xin;MAO Run;ZHANG Zheng-liang(Department of Mathematics and Statistics,Wuhan University,Wuhan 430072,China;Chongqing No.8 Secondary School,Chongqing 401120,China)

机构地区：[1]武汉大学数学与统计学院,武汉430072 [2]重庆市第八中学校,重庆401120

出　　处：《数学杂志》2020年第6期673-682,共10页Journal of Mathematics

基　　金：国家自然科学基金(NSFC11371283,11671076,11871382).

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Poincare不等式.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 Poincare inequalities.

关 键 词：Boltzmann测度 对数SOBOLEV不等式 传输不等式 POINCARE不等式 

分 类 号：O177[理学—数学]