Counterexamples to the $L^1$ and $L^{\infty }$ boundedness of the one-dimensional wave operators

Sisi Huang, Xiaohua Yao

It is well established that the wave operators $W_{\pm }(H,-\Delta )$ for the one-dimensional Schrödinger operator $H=-\Delta +V(x)$ are bounded on $L^p(\mathbb{R})$ for all $1<p<\infty$ in bot…