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 Riesz transform is denoted by T∗ = (– + V)– 1 2∇ . In this paper, we establish the boundedness for the operator T∗ and its commutator on the weighted Morrey spaces L α,V ,ω(R n) related to certain nonnegative potentials belonging to the reverse Hölder class Bq for n/2≤ q < n, where p′0 < p <∞ and 1 p0 = 1 q – 1 n .