Dans cette brève Note, on donne un raffinement de lʼinégalité de Brascamp–Lieb [1] dans le style de lʼextension de Houdré–Kagan [3] pour lʼinégalité de Poincaré en une dimension. Cette Note est inspirée par les travaux de Helffer et de Ledoux.
In this short note, we give a refinement of the Brascamp–Lieb inequality in the style of the Houdré–Kagan extension for the Poincaré inequality in one dimension. This is inspired by works by Helffer and by Ledoux.
Accepté le :
Publié le :
Ionel Popescu 1, 2
@article{CRMATH_2014__352_1_55_0, author = {Ionel Popescu}, title = {A refinement of the {Brascamp{\textendash}Lieb{\textendash}Poincar\'e} inequality in one dimension}, journal = {Comptes Rendus. Math\'ematique}, pages = {55--58}, publisher = {Elsevier}, volume = {352}, number = {1}, year = {2014}, doi = {10.1016/j.crma.2013.11.013}, language = {en}, }
Ionel Popescu. A refinement of the Brascamp–Lieb–Poincaré inequality in one dimension. Comptes Rendus. Mathématique, Volume 352 (2014) no. 1, pp. 55-58. doi : 10.1016/j.crma.2013.11.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.11.013/
[1] On extensions of the Brunn–Minkowski and Prékopa–Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation, J. Funct. Anal., Volume 22 (1976) no. 4, pp. 366-389
[2] Remarks on decay of correlations and Witten Laplacians, Brascamp–Lieb inequalities and semiclassical limit, J. Funct. Anal., Volume 155 (1998) no. 2, pp. 571-586
[3] Variance inequalities for functions of Gaussian variables, J. Theor. Probab., Volume 8 (1995) no. 1, pp. 23-30
[4] Lʼalgèbre de Lie des gradients itérés dʼun générateur markovien – Développements de moyennes et entropies, Ann. Sci. Éc. Norm. Super. (4), Volume 28 (1995) no. 4, pp. 435-460
- Free functional inequalities on the circle, Advances in Mathematics, Volume 330 (2018), p. 1101 | DOI:10.1016/j.aim.2017.10.021
- Refinements of the One Dimensional Free Poincaré Inequality, International Mathematics Research Notices, Volume 2015 (2015) no. 17, p. 8116 | DOI:10.1093/imrn/rnu189
Cité par 2 documents. Sources : Crossref
Commentaires - Politique