We establish the boundedness of some Schrödinger type operators on local generalized Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class.

No abstract

Let L = − + V be a Schrödinger operator, where the non-negative potential V belongs to the reverse Hölder class RH n/2 , let b belong to a new BMO θ (ρ) space, and let I L β be the fractional integral operator associated with L . In this paper, we study the boundedness of the operator I L β and its commutators [b,I L β ] with b ∈ BMO θ (ρ) on generalized Morrey spaces associated with Schrödinger operator M α,V p,ϕ and vanishing generalized Morrey spaces associated with Schrödinger operator V M α,V p,ϕ . We find the sufficient conditions on the pair (ϕ 1 ,ϕ 2 ) which ensures the boundedness of the operatorand (ϕ 1 ,ϕ 2 ) satisfies some conditions, we also show that the commutator operator (2010): 42B35, 35J10, 47H50. Mathematics subject classification