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

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 $({\Delta }^2+V(x))u(x)=0$.