Parameter θ-Type Marcinkiewicz Integral on Nonhomogeneous Weighted Generalized Morrey Spaces

Abstract

Let X,d,μ be a nonhomogeneous metric measure space satisfying the upper doubling and geometrically doubling conditions in the sense of Hytönen. In this setting, the author proves that parameter θ-type Marcinkiewicz integral Mθρ is bounded on the weighted generalized Morrey space Lp,ϕ,τω for p∈1,∞. Furthermore, the boudedness of Mθρ on weak weighted generalized Morrey space WLp,ϕ,τω is also obtained.