Bmo ρ (ω) spaces and Riesz transforms associated to Schrödinger operators

Abstract

We introduce the BMO-type space bmo ρ (ω) and establish the duality between h 1 (ω) and bmo ρ (ω), where ω ∈ A 1 , ∞ (ℝ n ) and ω’s locally behave as Muckenhoupt’s weights but actually include them. We also give the Fefferman-Stein type decomposition of bmo ρ (ω) with respect to Riesz transforms associated to Schrodinger operator ℒ, where ℒ = -Δ + V is a Schrodinger operator on ℝ n (n ⩾ 3) and V is a nonnegative function satisfying the reverse Holder inequality.