Piero D'Ancona, Luca Fanelli
Published 2005-09-26, updated 2005-09-29Version 3
Given a one dimensional perturbed Schroedinger operator H=-(d/dx)^2+V(x) we consider the associated wave operators W_+, W_- defined as the strong L^2 limits as s-> \pm\infty of the operators e^{isH} e^{-isH_0} We prove that the wave operators are bounded operators on L^p for all 1<p<\infty, provided (1+|x|)^2 V(x) is integrable, or else (1+|x|)V(x) is integrable and 0 is not a resonance. For p=\infty we obtain an estimate in terms of the Hilbert transform. Some applications to dispersive estimates for equations with variable rough coefficients are given.
The Hilbert Transform of a Measure
$β$-Boundedness, Semipassivity, and the KMS-Condition
$L^p$-boundedness of wave operators for $Δ^2 + V$ on ${\mathbb R}^4$
