We establish various estimates for the Schrödinger operator on Riemannian manifolds satisfying the doubling property and a Poincaré inequality, where is the Laplace-Beltrami operator and belongs to a reverse Hölder class. At the end of this paper we apply our result to Lie groups with polynomial growth.
@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://www.numdam.org/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://www.numdam.org/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://www.numdam.org/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, Serie 5, Volume 8 (2009) no. 4, pp. 725-765. http://www.numdam.org/item/ASNSP_2009_5_8_4_725_0/
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