$L^p$ Boundedness of the Scattering Wave Operators of Schr\"odinger Dynamics -- Part 2

We give another proof of the $L^p$ boundedness of scattering wave operators, at the low frequency part of the data. The proof also allows the control of the commutator of multiplication by $\mathrm{\mid }x\mathrm{\mid }$ with the wave operator in $L^p$. The method we develop here is geared to proving similar results for \emph{time dependent potentials}, complementing previous work focused on the high frequency part.