Sobolev inequalities for probability measures on the real line

• Autorzy: F. Barthe , C. Roberto
• Języki publikacji: EN

Abstrakty

EN

We give a characterization of those probability measures on the real line which satisfy certain Sobolev inequalities. Our starting point is a simpler approach to the Bobkov-Götze characterization of measures satisfying a logarithmic Sobolev inequality. As an application of the criterion we present a soft proof of the Latała-Oleszkiewicz inequality for exponential measures, and describe the measures on the line which have the same property. New concentration inequalities for product measures follow.

Kategorie tematyczne

• 60E15: Inequalities; stochastic orderings
• 26D10: Inequalities involving derivatives and differential and integral operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 159
• Numer: 3
• Strony: 481-497

Daty

wydano

2003

Twórcy

autor

F. Barthe

• CNRS, Laboratoire d'Analyse et Mathématiques Appliquées, UMR 8050, Universités de Marne-la-Vallée et de Paris 12-Val-de-Marne, Boulevard Descartes, Cité Descartes, Champs sur Marne, 77454 Marne-la-Vallée Cedex 2, France

autor

C. Roberto

• CNRS-Laboratoire d'Analyse et Mathématiques Appliquées, UMR 8050, Universités de Marne la Vallée et de Paris 12-Val-de-Marne, Boulevard Descartes, Cité Descartes, Champs sur Marne, 77454 Marne la Vallée Cedex 2, FRANCE

Identyfikatory

DOI

10.4064/sm159-3-9