The Lp boundedness of wave operators for Schrödinger operators with threshold singularities

Let H=−Δ+V be a Schrödinger operator on L2(Rn) with real-valued potential V for n>4 and let H0=−Δ. If V has sufficiently rapid decay, the wave operators defined as W±=s−limt→±∞⁡eitHe−itH0 are known to be bounded on Lp(Rn) for all 1≤p≤∞ if zero is not an eigenvalue, and on 1