Semi-classical functional calculus on manifolds with ends and weighted L p estimates
[Calcul fonctionnel semi-classique et estimations L p pondérées]
Bouclet, Jean-Marc
Annales de l'Institut Fourier, Tome 61 (2011), p. 1181-1223 / Harvested from Numdam
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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.

Publié le : 2011-01-01
DOI : https://doi.org/10.5802/aif.2638
Classification:  58J40
Mots clés: variété à bouts, estimations L p , opérateurs h-pseudodifférentiels 
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     author = {Bouclet, Jean-Marc},
     title = {Semi-classical functional calculus on manifolds with ends and weighted $L^p$ estimates},
     journal = {Annales de l'Institut Fourier},
     volume = {61},
     year = {2011},
     pages = {1181-1223},
     doi = {10.5802/aif.2638},
     zbl = {1236.58033},
     mrnumber = {2918727},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2011__61_3_1181_0}
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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) pp. 1181-1223. doi : 10.5802/aif.2638. http://gdmltest.u-ga.fr/item/AIF_2011__61_3_1181_0/

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