Fractional Maximal Operator Associated with Schrödinger Operator and its Commutators on Vanishing Generalized Morrey Spaces

Abstract

Let L = −△ + V be a Schrödinger operator, where the non-negative potential V belongs to the reverse Hölder class RHn/2, let b belong to a new BMOθ (ρ) space which is larger than the classical BMO space, and let Mβ,Vθ be the fractional maximal operator associated with L. In this paper, we study the boundedness of the operator Mβ,Vθ and its commutators [b, Mβ,Vθ] with (Formula presented) on generalized Morrey spaces (Formula presented) associated with Schrödinger operator and vanishing generalized Morrey spaces (Formula presented) associated with Schrödinger operator. We find the sufficient conditions on the pair (ϕ1, ϕ2) which ensures the boundedness of the operators Mβ,Vθ from one vanishing generalized Morrey space V Mp,ϕ1α,V to another (Formula presented).