Semi-classical functional calculus on manifolds with ends and weighted L p estimates
[Calcul fonctionnel semi-classique et estimations L p pondérées]
Annales de l'Institut Fourier, Tome 61 (2011) no. 3, pp. 1181-1223.

Pour une classe de variétés riemanniennes à bouts, nous donnons des développements semi-classiques de fonctions bornées du Laplacien. Nous étudions ensuite des propriétés de continuité L p de ces opérateurs et montrons en particulier que, bien qu’ils ne soient en général pas bornés sur L p , ils le sont toujours sur des espaces L p à poids convenables.

For a class of non compact Riemannian manifolds with ends, we give semi-classical expansions of bounded functions of the Laplacian. We then study related L p boundedness properties of these operators and show in particular that, although they are not bounded on L p in general, they are always bounded on suitable weighted L p spaces.

DOI : 10.5802/aif.2638
Classification : 58J40
Keywords: Manifold with ends, $L^p$ estimates, $h$-pseudodifferential operators
Mot clés : variété à bouts, estimations $L^p$, opérateurs $h$-pseudodifférentiels
Bouclet, Jean-Marc 1

1 Université Paul Sabatier - IMT UMR CNRS 5219 31062 Toulouse Cedex 9 (France)
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Bouclet, Jean-Marc. Semi-classical functional calculus on manifolds with ends and weighted $L^p$ estimates. Annales de l'Institut Fourier, Tome 61 (2011) no. 3, pp. 1181-1223. doi : 10.5802/aif.2638. http://www.numdam.org/articles/10.5802/aif.2638/

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