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

Abstract EN

Let X , d , μ be a metric measures space satisfying the upper doubling conditions and the geometrically doubling conditions in the senseof Hytönen.

Under the assumption that the dominating function satisfies the weak reverse doubling condition, the authors prove that Marcinkiewiczintegral with kernel satisfying certain stronger Hörmander-type condition is bounded on RBMO μ space.