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 RH _q 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<p≤1. We show also that the operators ∇; ²L ^-1 map the classical Hardy spaces Hp(Rn) into Hp(Rn) for a restricted range of p.