Dispersive estimates for fractional order Schrödinger operators

We prove dispersive bounds for fractional Schrödinger operators on Rⁿ of the form H=(-Δ)^α+V with V a real-valued, decaying potential and α∉ N. We derive pointwise bounds on the resolvent operators for all 0<α<n/2, a quantitative limiting absorption principle for 12<α<n/2, and establish global dispersive estimates in dimension n≥ 2 for the range n+1/4≤ α<n2.