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Article Dans Une Revue Studia Mathematica Année : 2003

Sobolev inequalities for probability measures on the real line

Résumé

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-Gotze characterization of measures satisfying a logarithmic Sobolev inequality. As an application of the criterion we present a soft proof of the Latala-Oleszkiewicz inequality for exponential measures, and describe the measures on the line which have the same property. New concentration inequalities for product measures follow.

Dates et versions

hal-00693117 , version 1 (01-05-2012)

Identifiants

Citer

Franck Barthe, Cyril Roberto. Sobolev inequalities for probability measures on the real line. Studia Mathematica, 2003, 159 (3), pp.481--497. ⟨10.4064/sm159-3-9⟩. ⟨hal-00693117⟩
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