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Improved interpolation inequalities on the sphere

Loss, Michael; Kowalczyk, Michal; Esteban, Maria J.; Dolbeault, Jean (2014), Improved interpolation inequalities on the sphere, Discrete and Continuous Dynamical Systems. Series S, 7, 4, p. 695-724. http://dx.doi.org/10.3934/dcdss.2014.7.695

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00867909
Date
2014
Journal name
Discrete and Continuous Dynamical Systems. Series S
Volume
7
Number
4
Publisher
AIMS
Pages
695-724
Publication identifier
Metadata
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Author(s)
Loss, Michael
Kowalczyk, Michal
Esteban, Maria J. cc
Dolbeault, Jean cc
Abstract (EN)
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.
Subjects / Keywords
spectral decomposition; hypercontractivity; heat equation; logarithmic Sobolev inequality; Gagliardo-Nirenberg inequalities; interpolation; Sobolev inequality