Hypercontractivity for log-subharmonic functions

TitreHypercontractivity for log-subharmonic functions
Type de publicationArticle de revue
AuteurGraczyk, Piotr , Kemp, Todd, Loeb, Jean-Jacques
PaysEtats-Unis
EditeurAcademic Press
VilleOrlando
TypeArticle scientifique dans une revue à comité de lecture
Année2010
LangueAnglais
Date2010/03/15
Numéro6
Pagination1785 - 1805
Volume258
Titre de la revueJournal of Functional Analysis
ISSN1096-0783
Mots-clésAnalyse, Probabilités et Statistique, Hypercontractivity, Log-Sobolev, Subharmonic
Résumé en anglais

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.

URL de la noticehttp://okina.univ-angers.fr/publications/ua126
DOI10.1016/j.jfa.2009.08.014
Lien vers le document

http://dx.doi.org/10.1016/j.jfa.2009.08.014

Titre abrégéJournal of Functional Analysis