Poincaré and Logarithmic Sobolev Inequalities for Nearly Radial Measures
| Autor: | Cattiaux, Patrick, Guillin, Arnaud, Wu, Liming |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2022 |
| Předmět: |
Mathematics - Functional Analysis
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] logconcave measure Poincaré inequality radial measure Applied Mathematics General Mathematics Super-Poincaré inequality [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] logarithmic Sobolev inequality Mathematics - Probability |
| Zdroj: | Acta Mathematica Sinica English Series Acta Mathematica Sinica English Series, 2022, 38 (8), pp.1377-1398. ⟨10.1007/s10114-022-0501-3⟩ |
| ISSN: | 1439-7617 1439-8516 |
| Popis: | If Poincar{\'e} inequality has been studied by Bobkov for radial measures, few is known about the logarithmic Sobolev inequalty in the radial case. We try to fill this gap here using different methods: Bobkov's argument and super-Poincar{\'e} inequalities, direct approach via L1-logarithmic Sobolev inequalities. We also give various examples where the obtained bounds are quite sharp. Recent bounds obtained by Lee-Vempala in the logconcave bounded case are refined for radial measures. |
| Databáze: | OpenAIRE |
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