Geodesic
Sobolev inequalities for probability measures on the real line
F. Barthe1 ; C. Roberto2
1 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
2 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
Studia Mathematica, Tome 159 (2003) no. 3, pp. 481-497 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm159-3-9
Keywords: characterization those probability measures real line which satisfy certain sobolev inequalities starting point simpler approach bobkov tze characterization measures satisfying logarithmic sobolev inequality application criterion present soft proof lata oleszkiewicz inequality exponential measures describe measures line which have property concentration inequalities product measures follow

F. Barthe 1 ; C. Roberto 2

1 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
2 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 
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 on the real line},
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 on the real line
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F. Barthe; C. Roberto. Sobolev inequalities for probability measures
 on the real line. Studia Mathematica, Tome 159 (2003) no. 3, pp. 481-497. doi: 10.4064/sm159-3-9

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