# American Institute of Mathematical Sciences

August  2014, 7(4): 695-724. doi: 10.3934/dcdss.2014.7.695

## Improved interpolation inequalities on the sphere

 1 Ceremade (UMR CNRS 7534), Université Paris Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris, Cédex 16 2 CEREMADE - UMR C.N.R.S. 7534, Université Paris IX-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France 3 Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMI 2807 CNRS), Universidad de Chile, Casilla 170 Correo 3, Santiago 4 School of Mathematics, Skiles Building, Georgia Institute of Technology, Atlanta GA 30332-0160, United States

Received  September 2013 Revised  December 2013 Published  February 2014

This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish some new results, clarify the range of applicability of the various existing methods and state several explicit estimates.
Citation: Jean Dolbeault, Maria J. Esteban, Michał Kowalczyk, Michael Loss. Improved interpolation inequalities on the sphere. Discrete & Continuous Dynamical Systems - S, 2014, 7 (4) : 695-724. doi: 10.3934/dcdss.2014.7.695
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