Let L = −∆ H n + V be a Schrödinger operator on the Heisenberg groups H n , where the non-negative potential V belongs to the reverse Hölder class RH Q/2 and Q is the homogeneous dimension of H n . Let b belong to a new BMO θ (H n , ρ) space, and let I L β be the fractional integral operator associated with L. In this paper, we study the boundedness of the operator I
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