On the Lp boundedness of wave operators for two-dimensional Schrödinger operators with threshold obstructions

Let H=−Δ+V be a Schrödinger operator on L2(R2) with real-valued potential V, and let H0=−Δ. If V has sufficient pointwise decay, the wave operators W±=s−limt→±∞⁡eitHe−itH0 are known to be bounded on Lp(R2) for all 1