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Sobolev inequalities for probability measures on the real line

Abstract : 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.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00693117
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Submitted on : Tuesday, May 1, 2012 - 8:25:34 PM
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Franck Barthe, Cyril Roberto. Sobolev inequalities for probability measures on the real line. Studia Mathematica, INSTYTUT MATEMATYCZNY * POLSKA AKADEMIA NAUK, 2003, 159 (3), pp.481--497. ⟨10.4064/sm159-3-9⟩. ⟨hal-00693117⟩

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