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<n2, a quantitative limiting absorption principle for 12<α<n2, and establish global dispersive estimates in dimension n 2 for the range n+14 α<n2.
Erdoğan et al. (Mon,) studied this question.