$L^{p}$ Boundedness of the Riesz transform related to Schrödinger operators on a manifold

Badr, Nadine; Ben Ali, Besma

Geodesic

Parcourir par

L^{p}

Boundedness of the Riesz transform related to Schrödinger operators on a manifold

Badr, Nadine ¹ ; Ben Ali, Besma ²

¹ Institut Camille Jordan, Université Claude Bernard Lyon 1, UMR du CNRS 5208, 43 boulevard du 11 novembre 1918, F-69622 Villeurbanne cedex, France
² Université de Paris-Sud, UMR du CNRS 8628, F-91405 Orsay cedex, France

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 4, pp. 725-765

Voir la notice de l'article provenant de la source Numdam

Résumé

We establish various $L^{p}$ estimates for the Schrödinger operator $- Δ + V$ on Riemannian manifolds satisfying the doubling property and a Poincaré inequality, where $Δ$ is the Laplace-Beltrami operator and $V$ belongs to a reverse Hölder class. At the end of this paper we apply our result to Lie groups with polynomial growth.

MR Zbl

Classification : 35J10, 42B37

Affiliations des auteurs :

Badr, Nadine ¹ ; Ben Ali, Besma ²

@article{ASNSP_2009_5_8_4_725_0,
     author = {Badr, Nadine and Ben Ali, Besma},
     title = {$L^{p}$ {Boundedness} of the {Riesz} transform related to {Schr\"odinger} operators on a manifold},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {725--765},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 8},
     number = {4},
     year = {2009},
     mrnumber = {2647910},
     zbl = {1200.35060},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2009_5_8_4_725_0/}
}

TY  - JOUR
AU  - Badr, Nadine
AU  - Ben Ali, Besma
TI  - $L^{p}$ Boundedness of the Riesz transform related to Schrödinger operators on a manifold
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2009
SP  - 725
EP  - 765
VL  - 8
IS  - 4
PB  - Scuola Normale Superiore, Pisa
UR  - http://geodesic.mathdoc.fr/item/ASNSP_2009_5_8_4_725_0/
LA  - en
ID  - ASNSP_2009_5_8_4_725_0
ER  -

%0 Journal Article
%A Badr, Nadine
%A Ben Ali, Besma
%T $L^{p}$ Boundedness of the Riesz transform related to Schrödinger operators on a manifold
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2009
%P 725-765
%V 8
%N 4
%I Scuola Normale Superiore, Pisa
%U http://geodesic.mathdoc.fr/item/ASNSP_2009_5_8_4_725_0/
%G en
%F ASNSP_2009_5_8_4_725_0

Badr, Nadine; Ben Ali, Besma. $L^{p}$ Boundedness of the Riesz transform related to Schrödinger operators on a manifold. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 4, pp. 725-765. http://geodesic.mathdoc.fr/item/ASNSP_2009_5_8_4_725_0/