Strichartz Estimates for the Schroedinger Equation with Time-Periodic L^{n/2} Potentials
Abstract
Description
We prove Strichartz estimates for the Schroedinger operator $H = -Δ+ V(t,x)$ with time-periodic complex potentials $V$ belonging to the scaling-critical space $L^{n/2}_x L^\infty_t$ in dimensions $n \ge 3$. This is done directly from estimates on the resolvent rather than using dispersive bounds, as the latter generally require a stronger regularity condition than what is stated above. In typical fashion, we project onto the continuous spectrum of the operator and must assume an absence of resonances. Eigenvalues are permissible at any location in the spectrum, including at threshold energies, provided that the associated eigenfunction decays sufficiently rapidly.
21 pages. Added L^2 stability statement to main theorem, as it was already implicit in the proof
21 pages. Added L^2 stability statement to main theorem, as it was already implicit in the proof