Riesz Transform Characterization of Weighted Hardy Spaces Associated with Schrödinger Operators

Abstract EN

We characterize the weighted local Hardy spaces h ρ 1 ( ω ) related to the critical radius function ρ and weights ω ∈ A 1 ρ , ∞ ( R n ) by localized Riesz transforms R ^ j ; in addition, we give a characterization of weighted Hardy spaces H L 1 ( ω ) via Riesz transforms associated with Schrödinger operator L , where L = - Δ + V is a Schrödinger operator on R n ( n ≥ 3 ) and V is a nonnegative function satisfying the reverse Hölder inequality.