The Lᵖ-continuity of wave operators for fractional order Schrödinger operators

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.