L^p boundedness of Riesz transform related to Schrödinger operators on a manifold

Nadine Badr (1) , Besma Ben Ali (2)

1 ICJ - Institut Camille Jordan
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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

Domaines: Analyse fonctionnelle [math.FA]

Nadine Badr, Besma Ben Ali. L^p boundedness of Riesz transform related to Schrödinger operators on a manifold. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2009, pp.725-765. ⟨hal-00863762⟩