Sharp interpolation inequalities on the sphere: new methods and consequences
Loss, Michael; Kowalczyk, Michal; Esteban, Maria J.; Dolbeault, Jean (2013), Sharp interpolation inequalities on the sphere: new methods and consequences, Chinese Annals of Mathematics. Series B, 34, 1, p. 99-112. http://dx.doi.org/10.1007/s11401-012-0756-6
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00739140
Journal nameChinese Annals of Mathematics. Series B
MetadataShow full item record
Abstract (EN)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.
Subjects / Keywordsheat equation; logarithmic Sobolev inequality; Gagliardo-Nirenberg inequalities; interpolation; Sobolev inequality
Showing items related by title and author.