The $L^p$-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 $L^p(\mathbb R^n)$ for all $1\leq p\leq\infty$ under conditions on the potential that depend on $n$ and $α$