Dispersive Estimates for the Schrödinger Equation with Potentials of Critical Regularity

Abstract

We prove L¹ → L^∞ dispersive estimates with a logarithmic loss of derivatives for the Schrödinger group e^{it(−Δ+V)} for a class of real-valued potentials V ∈ C^{(n−3)/2}(â„›ⁿ), V(x) = O(〈x〉^−δ), where n = 4, 5, Î´ > 3 if n = 4 and δ > 5 if n = 5.