A note on endpoint L^p-continuity of wave operators for classical and higher order Schrodinger operators

We consider the higher order Schrodinger operator H = (-Delta)(m) +V (x) inn dimensions with real-valued potential V when n > 2m, m E N. We adapt our recent results form > 1 to show that the wave operators are bounded on L-p(R-n) for the full the range 1 <= p <= infinity in both even and odd dimensions without assuming the potential is small. The approach used works without distinguishing even and odd cases, captures the endpoints p =1, infinity, and somehow simplifies the low energy argument even in the classical case of m = 1. (c) 2023 Elsevier Inc. All rights reserved.