Boundedness of commutators of Calderón-Zygmund operators on spaces with non-homogeneous metric measure

Let (X,d,\mu ) be a non-homogeneous metric measure space satisfying the geometrically doubling and the upper doubling conditions, by the properties of the non-homogeneous metric measure spaces, using the theory of boundedness for singular integral operators, based on the characterization of Herz spaces and the atomic and molecular decompesitions of Herz type Hardy spaces with non-homogeneous metric measure, the authors proved that the commutators generated by Calderon-Zygmund operators and Lipschitz functions are bounded on Herz type spaces with non-homogeneous metric measure.