# The L^p-continuity of the wave operators for the three dimensional Schroedinger operator

@inproceedings{Fanelli2007TheLO, title={The L^p-continuity of the wave operators for the three dimensional Schroedinger operator}, author={L. Fanelli}, year={2007} }

We consider a three dimensional perturbed Schrödinger operator H = −∆ + V (x), and the associated wave operators, that are defined as the strong L 2-limits lim t→±∞ e itH e −itH 0. We prove the boundedness of W ± as operators onto L p , for all p ∈ [1, ∞], provided the potential V is small in the Rollnik and Kato norms. We use this result to obtain sharp dispersive estimates for Schrödinger, wave and Klein-Gordon equations.

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