Boundedness of Marcinkiewicz Integrals on RBMO Spaces over Nonhomogeneous Metric Measure Spaces

Abstract

Let X,d,μ be a metric measures space satisfying the upper doubling conditions and the geometrically doubling conditions in the sense of Hytönen. Under the assumption that the dominating function satisfies the weak reverse doubling condition, the authors prove that Marcinkiewicz integral with kernel satisfying certain stronger Hörmander-type condition is bounded on RBMOμ space.