Fractional Poincaré inequalities for general measures

Clément Mouhot, Emmanuel Russ, Yannick Sire

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


We prove a fractional version of Poincaré inequalities in the context of Rn endowed with a fairly general measure. Namely we prove a control of an L2 norm by a non-local quantity, which plays the role of the gradient in the standard Poincaré inequality. The assumption on the measure is the fact that it satisfies the classical Poincaré inequality, so that our result is an improvement of the latter inequality. Moreover we also quantify the tightness at infinity provided by the control on the fractional derivative in terms of a weight growing at infinity. The proof goes through the introduction of the generator of the Ornstein-Uhlenbeck semigroup and some careful estimates of its powers. To our knowledge this is the first proof of fractional Poincaré inequality for measures more general than Lévy measures. © 2010 Elsevier Masson SAS.
Original languageEnglish (US)
Pages (from-to)72-84
Number of pages13
JournalJournal de Mathématiques Pures et Appliquées
Issue number1
StatePublished - Jan 2011
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: The first author would like to thank the Award No. KUK-I1-007-43, funded by the King Abdullah University of Science and Technology (KAUST) for the funding provided in Cambridge University.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


Dive into the research topics of 'Fractional Poincaré inequalities for general measures'. Together they form a unique fingerprint.

Cite this