(untitled) (Analysis in Theory and Applications, 2016)
Let H^n be the Heisenberg group and Q=2n+2 be its homogeneous dimension. In this paper, we consider the Schrödinger operator −∆_H^n +V, where Δ_H^n is the sub-Laplacian and V is the nonnegative potential belonging to the reverse Hölder class B_q_1 for q_1 ≥ Q/2. We show that the operators T_1 = V(−∆_H^n +V)^−1 and T_2 = V^1/2(−∆_H^n +V)^−1/2 are both bounded from H^1_L(H^n) into L^1(H^n). Our results are also valid on the stratified Lie group.