The $L^p$-boundedness of wave operators for four dimensional Schrödinger operators with threshold resonances

Kenji Yajima

We prove that the low energy parts of the wave operators $W_{\pm }$ for Schrödinger operators $H = -\lap + V(x)$ on ${\mathbb{R}}^4$ are bounded in $L^p({\mathbb{R}}^4)$ for $1<p\le 2$ and are unbounde…