Endpoint estimates for Riesz transforms of magnetic Schröedinger operators

Let A=-(∇-ia⃗)²+V be a magnetic Schrödinger operator acting on L²(Rⁿ), n≥1, where a⃗=(a₁,...,an) ∈L²loc and 0≤V∈L¹loc. Following [1], we define, by means of the area integral function, a Hardy space H¹A associated with A. We show that Riesz transforms (∂/∂xk -i a k)A⁻¹/² associated with A, k=1,...,n, are bounded from the Hardy space H¹A into L¹. By interpolation, the Riesz transforms are bounded on Lp for all 1