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Springer Verlag, Chinese Annals of Mathematics, Series B, 1(34), p. 99-112

DOI: 10.1007/s11401-012-0756-6

Partial Differential Equations: Theory, Control and Approximation, p. 225-242

DOI: 10.1007/978-3-642-41401-5_9

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Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences

Journal article published in 2013 by Jean Dolbeault ORCID, Maria J. Esteban, Michal Kowalczyk, Michael Loss
This paper is available in a repository.
This paper is available in a repository.

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Abstract

These notes are devoted to various considerations on a family of sharp interpolation inequalities on the sphere, which in dimension two and higher interpolate between Poincaré, logarithmic Sobolev and critical Sobolev (Onofri in dimension two) inequalities. We emphasize the connexion between optimal constants and spectral properties of the Laplace-Beltrami operator on the sphere. We shall address a series of related observations and give proofs based on symmetrization and the ultraspherical setting.