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

2008/12/06 by Nadine Badr, Badr, Nadine, Besma Ben Ali +1
Mathematics · #Advanced Harmonic Analysis Research #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.0812.1265

openalex publication_date 2008/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 on Lie groups with polynomial growth.

Related

• Riesz transform on manifolds and Poincaré inequalities
• Riesz transforms through reverse Hölder and Poincaré inequalities
• Maximal inequalities and Riesz transform estimates on L^p spaces for Schrödinger operators with nonnegative potentials
• Behaviour of Schrödinger Riesz transforms over smoothness spaces
• Boundedness from H¹ to L¹ of Riesz transforms on a Lie group of exponential growth