This paper is devoted to various considerations on a family of sharp interpo- lation inequalities on the sphere, which in dimension greater than 1 interpolate between Poincare, logarithmic Sobolev and critical Sobolev...This paper is devoted to various considerations on a family of sharp interpo- lation inequalities on the sphere, which in dimension greater than 1 interpolate between Poincare, 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 setting.展开更多
基金Project supported by ANR grants CBDif and NoNAP,the ECOS project (No. C11E07)the Chileanresearch grants Fondecyt (No. 1090103)Fondo Basal CMM Chile,Project Anillo ACT 125 CAPDEand the National Science Foundation (No.DMS 0901304)
文摘This paper is devoted to various considerations on a family of sharp interpo- lation inequalities on the sphere, which in dimension greater than 1 interpolate between Poincare, 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 setting.
