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

Let L = -+ V be a Schrödinger operator, where is the Laplacian on R n and the nonnegative potential V belongs to the reverse Hölder class B q for q ≥ n/2.The Riesz transform associated with the operator L is denoted by T = ∇(-+ V) -1 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 p,λ α,V,ω (R n ) related to certain nonnegative potentials belonging to the reverse Hölder class B q for n/2 ≤ q < n, where p 0 < p < ∞ and 1 p 0 = 1 q -1 n .