Title: Boundedness of second-order Riesz transforms on weighted Hardy and BMO spaces associated with Schrödinger operators
Abstract: Let d∈{3,4,5,...} and a weight w∈A ∞ ρ . We consider the second-order Riesz transform T=∇ 2 L -1 associated with the Schrödinger operator L=-Δ+V, where V∈RH σ with σ>d 2. We present three main results. First T is bounded on the weighted Hardy space H w,L 1 (ℝ d ) associated with L if w enjoys a certain stable property. Secondly T is bounded on the weighted BMO space BMO w,ρ (ℝ d ) associated with L if w also belongs to an appropriate doubling class. Thirdly BMO w,ρ (ℝ d ) is the dual of H w,L 1 (ℝ d ) when w∈A 1 ρ .