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| Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences |
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Citation： |
Jean DOLBEAULT,Maria J. ESTEBAN,Michal KOWALCZYK,Michael LOSS.Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences[J].Chinese Annals of Mathematics B,2013,34(1):99~112 |
| Page view： 3328
Net amount： 1852 |
Authors： |
Jean DOLBEAULT; Maria J. ESTEBAN; Michal KOWALCZYK; Michael LOSS; |
Foundation： |
ANR grants CBDif and NoNAP, the ECOS project (No. C11E07), the Chilean research grants Fondecyt (No. 1090103), Fondo Basal CMM-Chile, Project Anillo ACT-125 CAPDE and the National Science Foundation (No. DMS-0901304). |
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| Abstract： |
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 Poincar\'e, 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. |
Keywords： |
Sobolev inequality, Interpolation, Gagliardo-Nirenberg inequality,Logarithmic Sobolev inequality, Heat equation |
Classification： |
26D10, 46E35, 58E35 |
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