For a non-homogeneous metric measure space satisfying the upper doubling and the geometrically doubling conditions,the molecular Herz-Morrey-Hardy spaces on the non-homogeneous metric measure space are introduced.The decomposition of the molecular Herz-Morrey-Hardy spaces is discussed.Then,by the properties of the non-homogeneous metric measure space,the characteristics of atom block and molecule block,and the properties of discrete coefficients,the equivalent for the atomic Herz-Morrey-Hardy spaces and the molecular Herz-Morrey-Hardy spaces is proved.In another words,this is the molecular characterization of the Herz-Morrey-Hardy spaces on non-homogeneous metric measure space.
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