Endpoint estimates for Riesz transforms of magnetic Schrödinger operators

Abstract

Let $A=-(\nabla-i\vec{a})^2+V$ be a magnetic Schrödinger operator acting on L²(Rⁿ), n≥1, where $\vec{a}=(a_1,\cdots,a_n)\in L^2_{\rm loc}$ and 0≤V∈L¹_loc. Following [1], we define, by means of the area integral function, a Hardy space H¹_A associated with A. We show that Riesz transforms (∂/∂x_k-ia_k)A^-1/2 associated with A, $k=1,\cdots,n$, are bounded from the Hardy space H¹_A into L¹. By interpolation, the Riesz transforms are bounded on L^p for all 1< p≤2.