Boundedness of Commutators of Marcinkiewicz Integrals on Nonhomogeneous Metric Measure Spaces

摘要

Let be a metric measure space satisfying the upper doubling condition and geometrically doubling condition in the sense of Hyt??nen. The aim of this paper is to establish the boundedness of commutator generated by the Marcinkiewicz integral and Lipschitz function . The authors prove that is bounded from the Lebesgue spaces to weak Lebesgue spaces for , from the Lebesgue spaces to the spaces for , and from the Lebesgue spaces to the Lipschitz spaces for . Moreover, some results in Morrey spaces and Hardy spaces are also discussed.