The Hardy space H 1 on non-homogeneous metric spaces

Source abstract

Abstract Let ( , d , μ) be a metric measure space and satisfy the so-called upper doubling condition and the geometrical doubling condition. We introduce the atomic Hardy space H 1 (μ) and prove that its dual space is the known space RBMO(μ) in this context. Using this duality, we establish a criterion for the boundedness of linear operators from H 1 (μ) to any Banach space. As an application of this criterion, we obtain the boundedness of Calderón–Zygmund operators from H 1 (μ) to L 1 (μ).