Riesz transforms associated to Schrödinger operators on weighted Hardy spaces

Abstract

Let w be some A p weight and enjoy reverse Hölder inequality, and let L = − Δ + V be a Schrödinger operator on R n , where V ∈ L loc 1 ( R n ) is a non-negative function on R n . In this article we introduce weighted Hardy spaces H L , w 1 ( R n ) associated to L in terms of the area function characterization, and prove their atomic characters. We show that the Riesz transform ∇ L − 1 / 2 associated to L is bounded on L w p ( R n ) for 1 < p < 2 , and bounded from H L , w 1 ( R n ) to the classical weighted Hardy space H w 1 ( R n ) .