Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
Volume 7, Issue 4, Pages 695-724Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdss.2014.7.695
Keywords
Sobolev inequality; interpolation; Gagliardo-Nirenberg inequalities; logarithmic Sobolev inequality; heat equation; hypercontractivity; spectral decomposition
Categories
Funding
- ANR
- AmSud QUESP project
- ECOS [C11E07]
- FONDECYT [1130126]
- Fondo Basal CMM
- NSF [DMS-1301555]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1301555] Funding Source: National Science Foundation
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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.
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