Some Remarks on Weighted Logarithmic Sobolev Inequality

被引：15

作者：

Cattiaux, Patrick ^{[1
]}

Guillin, Arnaud ^{[2
]}

Wu, Li-Ming ^{[2
]}

机构：

[1] Univ Toulouse 3, Inst Math Toulouse, CNRS UMR 5219, F-31062 Toulouse 09, France

[2] Univ Blaise Pascal, Lab Math, CNRS UMR 6620, F-63177 Aubiere, France

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2011年 / 60卷 / 06期

关键词：

Lyapunov functions; Talagrand transportation information inequality; logarithmic Sobolev inequality; MARKOV PROCESS EXPECTATIONS; FUNCTIONAL INEQUALITIES; ASYMPTOTIC EVALUATION; PROBABILITY-MEASURES; MODERATE DEVIATIONS; SPECTRAL THEORY; FAST DIFFUSION; CONVERGENCE; HYPERCONTRACTIVITY; STABILITY;

D O I：

10.1512/iumj.2011.60.4405

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give here a simple proof of weighted logarithmic Sobolev inequality, for example for Cauchy type measures, with optimal weight, sharpening results of Bobkov-Ledoux [12]. Some consequences are also discussed.

引用

页码：1885 / 1904

页数：20

共 50 条

[21] Lipschitz constants and logarithmic Sobolev inequality
Fujita, Yasuhiro
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 408 (02) : 705 - 712
[22] Logarithmic Sobolev inequality for symmetric forms
陈木法
ScienceinChina,SerA., 2000, Ser.A.2000 (06) : 601 - 608
[23] A Stein deficit for the logarithmic Sobolev inequality
Michel Ledoux
Ivan Nourdin
Giovanni Peccati
Science China Mathematics, 2017, 60 : 1163 - 1180
[24] A Stein deficit for the logarithmic Sobolev inequality
LEDOUX Michel
NOURDIN Ivan
PECCATI Giovanni
ScienceChina(Mathematics), 2017, 60 (07) : 1163 - 1180
[25] A Generalization of the Logarithmic Gross–Sobolev Inequality
Sh. M. Nasibov
Doklady Mathematics, 2019, 100 : 329 - 331
[26] DEFICIT ESTIMATES FOR THE LOGARITHMIC SOBOLEV INEQUALITY
Indrei, Emanuel
Kim, Daesung
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2021, 34 (7-8) : 437 - 466
[27] A logarithmic Sobolev inequality on the real line
Pearson, JM
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 125 (11) : 3339 - 3345
[28] SOME REMARKS ON EXTENSION-THEOREMS FOR WEIGHTED SOBOLEV SPACES
CHUA, SK
ILLINOIS JOURNAL OF MATHEMATICS, 1994, 38 (01) : 95 - 126
[29] Geometric asymptotics and the logarithmic Sobolev inequality
Beckner, W
FORUM MATHEMATICUM, 1999, 11 (01) : 105 - 137
[30] Bounds on the deficit in the logarithmic Sobolev inequality
Bobkov, S. G.
Gozlan, N.
Roberto, C.
Samson, P. -M.
JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 267 (11) : 4110 - 4138

← 1 2 3 4 5 →