Estimates for Parabolic Schrödinger Operators with Certain Nonnegative Potentials

In this paper, the parabolic Schrödinger operator P=∂ₜ-+V(x) on Rⁿ⁺¹ is considered, where n≥3, nonnegative potential V belongs to the reverse Hölder class RHq with q ≥ n /2. The Lᵖ boundedness of operators VαP-β, Vα∇P-β and their adjoint operators are established.