01-319 Arne Jensen and Kenji Yajima

A remark on $L^p$-boundedness of wave operators for two dimensional Schroedinger operators (220K, PDF) Sep 5, 01

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Abstract. Let $H=-\delta+V$ be a two-dimensional Schr\"{o}dinger operator with a real potential $V(x)$ satisfying the decay condition $|V(x)|\leq C (1+|x|)^{-\delta}$, $\delta>6$. Assume that $H$ has no zero resonances or zero bound states. We prove that the wave operators $W_{\pm}$ are bounded in $L^p(\mathbf{R}^2)$, $1<p<\infty$. The main result in this paper is the removal of the condition $\int V(x) dx\neq0$, imposed in a previous paper (K. Yajima, Commun. Math. Phys. 208 (1999), 125-152).

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