The molecular characterization of the Hardy space H1H1 on non-homogeneous metric measure spaces and its application

Let (X,d,μ)(X,d,μ) be a non-homogeneous metric measure space, which means that (X,d,μ)(X,d,μ) is a metric measure space satisfying both the geometrically doubling and the upper doubling conditions. In this paper, the authors introduce the atomic Hardy space H˜atb1,p(μ) via the discrete coefficient K˜B,S(ρ) for ρ∈(1,∞)ρ∈(1,∞) and balls B⊂SB⊂S of XX. Then, the authors establish the corresponding molecular characterization of H˜atb1,p(μ) via a constructive way. As an application, the authors obtain the boundedness of Calderón–Zygmund operators on H˜atb1,p(μ). Moreover, the authors give a sufficient condition to guarantee that H˜atb1,p(μ) coincides with the existing atomic Hardy space Hatb1,p(μ).