Accéder directement au contenu Accéder directement à la navigation
Article dans une revue

Hypercontractivity for log-subharmonic functions

Abstract :

We prove strong hypercontractivity (SHC) inequalities for logarithmically subharmonic functions on R n and different classes of measures: Gaussian measures on R n , symmetric Bernoulli and symmetric uniform probability measures on R , as well as their convolutions. Surprisingly, a slightly weaker strong hypercontractivity property holds for any symmetric measure on R . A log-Sobolev inequality (LSI) is deduced from the (SHC) for compactly supported measures on R n , still for log-subharmonic functions. An analogous (LSI) is proved for Gaussian measures on R n and for other measures for which we know the (SHC) holds. Our log-Sobolev inequality holds in the log-subharmonic category with a constant smaller than the one for Gaussian measure in the classical context.

Type de document :
Article dans une revue
Liste complète des métadonnées

https://hal.univ-angers.fr/hal-03040216
Contributeur : Okina Université d'Angers <>
Soumis le : vendredi 4 décembre 2020 - 11:20:42
Dernière modification le : samedi 5 décembre 2020 - 03:20:55

Lien texte intégral

Identifiants

Collections

Citation

Piotr Graczyk, Todd Kemp, Jean-Jacques Loeb. Hypercontractivity for log-subharmonic functions. Journal of Functional Analysis, 2010, 258 (6), pp.1785 - 1805. ⟨10.1016/j.jfa.2009.08.014⟩. ⟨hal-03040216⟩

Partager

Métriques

Consultations de la notice

13