Dispersive Bounds for the three-dimensional Schrodinger equation with almost critical potentials
Michael Goldberg
Abstract
We prove a dispersive estimate for the time-independent Schrodinger operator H = -Δ+ V in three dimensions. The potential V(x) is assumed to lie in the intersection Lp(R3) Lq(R3), p < 3/2 < q, and also to satisfy a generic zero-energy spectral condition. This class, which includes potentials that have pointwise decay |V(x)| < C(1+|x|)-2-ε, is nearly critical with respect to the natural scaling of the Laplacian. No additional regularity, decay, or positivity of V is assumed.
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