We consider fractional Schrödinger operators H= (-Δ) ^α+V (x) in n dimensions with real-valued potential V when n>2α, α>1. We show that the wave operators extend to bounded operators on Lᵖ (Rⁿ) for all 1 p under conditions on the potential that depend on n and α analogously to the case when α N. As a consequence, we deduce a family of dispersive and Strichartz estimates for the perturbed fractional Schrödinger operator.
Erdoğan et al. (Mon,) studied this question.