For higher-order Schrödinger operators with a threshold eigenvalue in dimensions 2m < n ≤ 4m, the wave operators are bounded on L^p for the natural range, with extended ranges and a new L∞ endpoint under extra orthogonality conditions.
Agmon, Spectral properties of Schr¨ odinger operators and scattering theory.Ann
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$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues
For higher-order Schrödinger operators with a threshold eigenvalue in dimensions 2m < n ≤ 4m, the wave operators are bounded on L^p for the natural range, with extended ranges and a new L∞ endpoint under extra orthogonality conditions.