Abstract: Let (X,d,μ) be a nonhomogeneous metric measure space satisfying the upper doubling and the geometrically doubling conditions. For a class of MorreyHerz spaces on the nonhomogeneous metric measure spaces, by using the properties of the nonhomogeneous metric measure spaces and the theory of boundedness for singular integral operators on the L^p spaces, we proved the boundedness of the Marcinkiewiczintegral operator and its commutator generated by RBMO function on the Morrey-Herz spaces with nonhomogeneous metric measure.

Key words:  , non-homogeneous metric measure space, MorreyHerz space, Marcinkiewicz integral, commutator, boundedness