Hardy spaces related to Schrödinger operators with potentials which are sums of Lp-functions (original) (raw)

We investigate the Hardy space H 1 L associated to the Schrödinger operator L = −∆ + V on R n , where V = d j=1 Vj. We assume that each Vj depends on variables from a linear subspace Vj of R n , dim Vj ≥ 3, and Vj belongs to L q (Vj) for certain q. We prove that there exist two distinct isomorphisms of H 1 L with the classical Hardy space. As a corollary we deduce a specific atomic characterization of H 1 L. We also prove that the space H 1 L is described by means of the Riesz transforms RL,i = ∂iL −1/2 .