On the $L^p$ boundedness of wave operators for four-dimensional Schrödinger Operators with a threshold eigenvalue

Michael Goldberg, William R. Green

Let $H=-\Delta +V$ be a Schrödinger operator on $L^2({\mathbb{R}}^4)$ with real-valued potential $V$, and let $H_0=-\Delta$. If $V$ has sufficient pointwise decay, the wave operators $W_{\pm}=s-…