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

Abstract

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 0 < η < n m , n m η < 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.