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

We consider the higher order Schrödinger operator H=(−Δ)^m+V(x) in n dimensions with real-valued potential V when n>2m, m∈N. We adapt our recent results for m>1 to show that the wave operators are bounded on L^p(Rⁿ) for the full the range 1≤p≤∞ 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,∞, and somehow simplifies the low energy argument even in the classical case of m=1.