A Remark on Lp-Boundedness of Wave Operators¶for Two Dimensional Schrödinger Operators

Let H=−Δ+V be a two dimensional Schr?dinger operator with a real potential V(x) satisfying the decay condition , δ > 6. Let H ₀=−Δ. We show that the wave operators are bounded in L ^p (R ²) under the condition that H has no zero resonances or bound states. In this paper the condition , imposed in a previous paper (K. Yajima, Commun. Math. Phys. 208, 125–152 (1999)), is removed. Received: 13 September 2001 / Accepted: 15 October 2001