$H^1$ BOUNDEDNESS FOR RIESZ TRANSFORM RELATED TO SCHRÖDINGER OPERATOR ON NILPOTENT GROUPS

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

We establish various Lp estimates for the Schrödinger operator −∆ + V on Riemannian manifolds satisfying the doubling property and a Poincaré inequality, where ∆ 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.

Boundedness for Riesz transform associated with Schrödinger operators and its commutator on weighted Morrey spaces related to certain nonnegative potentials

*Correspondence: [email protected] School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China Abstract Let L = – + V be a Schrödinger operator, where is the Laplacian on Rn and the nonnegative potential V belongs to the reverse Hölder class Bq for q≥ n/2. The Riesz transform associated with the operator L is denoted by T =∇(– + V)– 2 and the dual Ri...

L Boundedness of Commutators of Riesz Transforms Associated to Schrödinger Operator

Abstract: In this paper we consider Lp boundedness of some commutators of Riesz transforms associated to Schrödinger operator P = −∆+ V (x) on Rn, n ≥ 3. We assume that V (x) is non-zero, nonnegative, and belongs to Bq for some q ≥ n/2. Let T1 = (−∆ + V ) −1V, T2 = (−∆ + V )−1/2V 1/2 and T3 = (−∆+ V ) −1/2∇. We obtain that [b, Tj ] (j = 1, 2, 3) are bounded operators on Lp(Rn) when p ranges in ...

Riesz Transform and Riesz Potentials for Dunkl Transform

Analogous of Riesz potentials and Riesz transforms are defined and studied for the Dunkl transform associated with a family of weighted functions that are invariant under a reflection group. The L boundedness of these operators is established in certain cases.

On the (p,q)-Boundedness of Nonisotropic Spherical Riesz Potentials