Improved interpolation inequalities on the sphere

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Date
2014
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http://hal.archives-ouvertes.fr/hal-00867909
Indexation documentaire
Analyse
Subject
spectral decomposition; hypercontractivity; heat equation; logarithmic Sobolev inequality; Gagliardo-Nirenberg inequalities; interpolation; Sobolev inequality
Nom de la revue
Discrete and Continuous Dynamical Systems. Series S
Volume
7
Numéro
4
Date de publication
2014
Pages article
695-724
Nom de l'éditeur
AIMS
DOI
http://dx.doi.org/10.3934/dcdss.2014.7.695
URI
https://basepub.dauphine.fr/handle/123456789/11917
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Auteur
Loss, Michael
Kowalczyk, Michal
Esteban, Maria J.
Dolbeault, Jean
Type
Article accepté pour publication ou publié
Résumé en anglais
This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish some new results, clarify the range of applicability of the various existing methods and state several explicit estimates.