Herz type Hardy spaces on non-homogeneous metric measure space

Abstract

Let $(\mathcal{X},d,\mu)$ be a non-homogeneous metric measure spacesatisfying both the geometrically doubling and the upper doublingconditions. In this paper, the Herz spaces on the non-homogeneousmetric measure space are introduced. Then the decomposition of theHerz space by the central blocks is obtained. The atomic Herz typeHardy spaces and the molecular Herz type Hardy spaces on thenon-homogeneous metric measure space via the discrete coefficient${\widetilde~K}_{B,S}^{(\rho),p}$ are also defined. In addition, theequivalence of the atomic Herz type Hardy spaces and the molecularHerz type Hardy spaces is established. As the applicationsof these spaces, some boundedness of Calderon-Zygmund operatorson the Herz type Hardy spaces are discussed.