The weighted estimates for the operators Vα(−ΔG+V)−β and Vα∇G(−ΔG+V)−β on the stratified Lie group G

In this paper we consider the Schrödinger operator −ΔG+V on the stratified Lie group G where the nonnegative potential V belongs to the reverse Hölder class Bq1 for some and Q is the homogeneous dimension of G. The weighted Lp–Lq estimates for the operators Vα(−ΔG+V)−β and Vα∇G(−ΔG+V)−β are obtained.