Sharp Beckner-type inequalities for Cauchy and spherical distributions - Archive ouverte HAL Access content directly
Journal Articles Studia Mathematica Year : 2019

Sharp Beckner-type inequalities for Cauchy and spherical distributions

Abstract

Using some harmonic extensions on the upper-half plane, and probabilistic representations, and curvature-dimension inequalities with some negative dimensions, we obtain some new opimal functional inequalities of the Beckner type for the Cauchy type distributions on the Euclidean space. These optimal inequalities appear to be equivalent to some non tight optimal Beckner inequalities on the sphere, and the family appear to be a new form of the Sobolev inequality.
Fichier principal
Vignette du fichier
HAL-bakry-gentil-scheffer3.pdf (350.2 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Comment : Ce pdf est la version preprint de l'article (version soumise à l'éditeur, avant peer-reviewing).
Loading...

Dates and versions

hal-01761215 , version 1 (08-04-2018)
hal-01761215 , version 2 (14-12-2018)
hal-01761215 , version 3 (15-01-2019)

Identifiers

Cite

Dominique Bakry, Ivan Gentil, Grégory Scheffer. Sharp Beckner-type inequalities for Cauchy and spherical distributions. Studia Mathematica, 2019, 251 (3), pp.219-245. ⟨10.4064/sm180503-17-1⟩. ⟨hal-01761215v3⟩
300 View
400 Download

Altmetric

Share

Gmail Facebook X LinkedIn More