The weighted estimates for the operators and on the stratified Lie group G

In this paper we consider the Schrödinger operator − Δ G + V on the stratified Lie group G where the nonnegative potential V belongs to the reverse Hölder class B q 1 for some q 1 ⩾ Q 2 and Q is the homogeneous dimension of G. The weighted L p – L q estimates for the operators V α ( − Δ G + V ) − β and V α ∇ G ( − Δ G + V ) − β are obtained.