The $L^{p}$-boundedness of wave operators for fourth order Schrödinger operators on $\R^{4}$

Abstract

We prove that the wave operators of the scattering theory for the fourth order Schrö­dinger operator \Delta^{2} + V(x) on {\mathbb{R}}^{4} are bounded in L^{p}({\mathbb{R}}^{4}) for the set of p ’s of (1,\infty) depending on the kind of spectral singularities of H at zero which can be described by the space of bounded solutions of (\Delta^{2} + V(x))u(x)=0 .

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