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 boundedness properties of these operators and show in particular that, although they are not bounded on in general, they are always bounded on suitable weighted spaces.
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 de ces opérateurs et montrons en particulier que, bien qu’ils ne soient en général pas bornés sur , ils le sont toujours sur des espaces à poids convenables.
Keywords: Manifold with ends, $L^p$ estimates, $h$-pseudodifferential operators
Mot clés : variété à bouts, estimations $L^p$, opérateurs $h$-pseudodifférentiels
@article{AIF_2011__61_3_1181_0, author = {Bouclet, Jean-Marc}, title = {Semi-classical functional calculus on manifolds with ends and weighted $L^p$ estimates}, journal = {Annales de l'Institut Fourier}, pages = {1181--1223}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {61}, number = {3}, year = {2011}, doi = {10.5802/aif.2638}, zbl = {1236.58033}, mrnumber = {2918727}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2638/} }
TY - JOUR AU - Bouclet, Jean-Marc TI - Semi-classical functional calculus on manifolds with ends and weighted $L^p$ estimates JO - Annales de l'Institut Fourier PY - 2011 SP - 1181 EP - 1223 VL - 61 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2638/ DO - 10.5802/aif.2638 LA - en ID - AIF_2011__61_3_1181_0 ER -
%0 Journal Article %A Bouclet, Jean-Marc %T Semi-classical functional calculus on manifolds with ends and weighted $L^p$ estimates %J Annales de l'Institut Fourier %D 2011 %P 1181-1223 %V 61 %N 3 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2638/ %R 10.5802/aif.2638 %G en %F AIF_2011__61_3_1181_0
Bouclet, Jean-Marc. Semi-classical functional calculus on manifolds with ends and weighted $L^p$ estimates. Annales de l'Institut Fourier, Volume 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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