Weighted Estimates for Marcinkiewicz Integral Operator Associated with Schrödinger Operator and Its Commutator on Generalized Fractional Morrey Spaces

The aim of this paper is to investigate the boundedness of a Marcinkiewicz integral operator μ j ℒ associated with Schrödinger operator and its commutator on weighted generalized fractional Morrey spaces L p,η,φ ( ℝ n ,ω ) . Under assumption that the function φ satisfies doubling conditions, the author proves that the μ j ℒ is bounded on spaces L p,η,φ ( ℝ n ,ω ) , where 0η n m , n mη p n η , and ω∈ A p ρ,θ ( ℝ n ) . Furthermore, the boundedness of the commutator [ b, μ j ℒ ] formed by b∈BMO( ℝ n ) and the μ j ℒ on spaces L p,η,φ ( ℝ n ,ω ) is also obtained.