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
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00867909
Journal nameDiscrete and Continuous Dynamical Systems. Series S
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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 / Keywordsspectral decomposition; hypercontractivity; heat equation; logarithmic Sobolev inequality; Gagliardo-Nirenberg inequalities; interpolation; Sobolev inequality
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