Refined inequalities on graded Lie groups

Hajer Bahouri; Clotilde Fermanian-Kammerer; Isabelle Gallagher

doi:10.1016/j.crma.2012.04.014

Harmonic Analysis

Refined inequalities on graded Lie groups

Presented by: Jean-Michel Bony

Hajer Bahouri ¹; Clotilde Fermanian-Kammerer ¹; Isabelle Gallagher ²

¹ LAMA UMR CNRS 8050, université Paris-Est Créteil, 61, avenue du Général de Gaulle, 94010 Créteil cedex, France
² Institut de mathématiques UMR 7586, université Paris Diderot (Paris 7), 175, rue du Chevaleret, 75013 Paris, France

Comptes Rendus. Mathématique, Volume 350 (2012) no. 7-8, pp. 393-397.

Abstract
Résumé

We construct a Littlewood–Paley decomposition associated to a Rockland operator on graded Lie groups, which allows us to deduce refined Gagliardo–Nirenberg, Sobolev and Hardy inequalities.

On construit une décomposition de Littlewood–Paley associée à un opérateur de Rockland sur les groupes de Lie gradués, qui permet de déduire des inégalités précisées de type Gagliardo–Nirenberg, Sobolev et Hardy.

Received: 2012-03-12
Accepted: 2012-04-17
Published online: 2012-04-01

DOI: 10.1016/j.crma.2012.04.014

Author's affiliations:

Hajer Bahouri ¹; Clotilde Fermanian-Kammerer ¹; Isabelle Gallagher ²

¹ LAMA UMR CNRS 8050, université Paris-Est Créteil, 61, avenue du Général de Gaulle, 94010 Créteil cedex, France
² Institut de mathématiques UMR 7586, université Paris Diderot (Paris 7), 175, rue du Chevaleret, 75013 Paris, France

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     title = {Refined inequalities on graded {Lie} groups},
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Hajer Bahouri; Clotilde Fermanian-Kammerer; Isabelle Gallagher. Refined inequalities on graded Lie groups. Comptes Rendus. Mathématique, Volume 350 (2012) no. 7-8, pp. 393-397. doi : 10.1016/j.crma.2012.04.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.04.014/

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