## The $L^p$-continuity of Wave Operators for One Dimensional SchrÃ¶dinger Operators

J. Math. Sci. Univ. Tokyo
Vol. 7 (2000), No. 2, Page 221--240.

Artbazar, Galtbayar ; Yajima, Kenji
The $L^p$-continuity of Wave Operators for One Dimensional SchrÃ¶dinger Operators
We consider the wave operators $W_\pm u = {\rm s-} \lim_{t \to \pm \infty} e^{itH}e^{-itH_0}u$ for a pair of \Schr operators ${\dsize H_0= -\frac{d^2}{dx^2}}$ and $H=H_0+V(x)$ on the line $\rbf$. We show that $W_\pm$ is bounded in $L^p(\rbf)$ for any \$1