For odd n ≤ 4m-1, the L^p range of the wave operators for (-Δ)^m+V is 1<p<∞ for regular or subcritical resonances, and shrinks to 1<p<p_k for stronger resonances, with p_k = n/(n-2m+k+k_c-1); the range is shown sharp.
Beceanu,Structure of wave operators for a scaling-critiacal class of potentials, Amer
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The $L^p$-boundedness of wave operators for higher order Schr\"odinger operator with zero singularities in low odd dimensions
For odd n ≤ 4m-1, the L^p range of the wave operators for (-Δ)^m+V is 1<p<∞ for regular or subcritical resonances, and shrinks to 1<p<p_k for stronger resonances, with p_k = n/(n-2m+k+k_c-1); the range is shown sharp.