Harmonic Analysis
Spectral multipliers on some rank one NA-groups with roots not all positive
Comptes Rendus. Mathématique, Volume 337 (2003) no. 12, pp. 767-770.

We consider a particular class of (non-unimodular) rank one NA-groups with roots not all positive, and we show that, on each of these groups, there exists a distinguished left invariant sub-Laplacian which admits a Lp-differentiable functional calculus for every p∈[1,+∞].

Nous considérons une certaine classe de groupes de Lie (non-unimodulaires) de type NA de rang un avec des racines non toutes positives, et nous montrons que, sur chacun de ces groupes, il existe un sous-laplacien invariant à gauche particulier qui admet un calcul fonctionnel Lp-différentiable pour tout p∈[1,+∞].

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Accepted:
Published online:
DOI: 10.1016/j.crma.2003.10.020
David-Guillou, Emilie 1

1 Université Pierre et Marie Curie – Paris VI, institut de mathématiques, 4, place Jussieu, 75252 Paris cedex 05, France
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David-Guillou, Emilie. Spectral multipliers on some rank one NA-groups with roots not all positive. Comptes Rendus. Mathématique, Volume 337 (2003) no. 12, pp. 767-770. doi : 10.1016/j.crma.2003.10.020. http://www.numdam.org/articles/10.1016/j.crma.2003.10.020/

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