The Hardy Space H¹ on Non-homogeneous Metric Spaces

الأصل · EN

Let (X, d, μ) be a metric measure space and satisfy the so-called upper doubling condition and the geometrical doubling condition. In this paper, we introduce the atomic Hardy space H¹(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 H¹(μ) to any Banach space. As an application of this criterion, we obtain the boundedness of Calderón--Zygmund operators from H¹(μ) to L¹(μ).