Second order Riesz transforms associated to the Schrödinger operator for p⩽1

Let L=−Δ+V be the Schrödinger operator on Rn, where V belongs to the class of reverse Hölder weights RHq for some q>max{2,n/2}. We show that the second order Riesz transforms ∇2L−1 and VL−1 are bounded from the Hardy spaces HLp(Rn) associated to L into Lp(Rn) for 0