Lp estimate for parabolic Schrödinger operator with certain potentials

The parabolic Schrödinger operator P=∂∂t−Δ+V on parabolic spaces Rn×[0,T] is considered. The boundedness of the operator ∇2(∂∂t−Δ+V)−1 on Lp(Rn×[0,T]) is obtained.