Sharp Interpolation Inequalities on the Sphere : New Methods and Consequences

@inproceedings{Dolbeault2012SharpII,
  title={Sharp Interpolation Inequalities on the Sphere : New Methods and Consequences},
  author={Jean Dolbeault and Maria J. Esteban and Michal Kowalczyk and Michael Loss},
  year={2012}
}
This paper is devoted to various considerations on a family of sharp interpolation inequalities on the sphere, which in dimension greater than 1 interpolate between Poincaré, logarithmic Sobolev and critical Sobolev (Onofri in dimension two) inequalities. The connection between optimal constants and spectral properties of the Laplace-Beltrami operator on the sphere is emphasized. The authors address a series of related observations and give proofs based on symmetrization and the ultraspherical… CONTINUE READING