The L^p-boundedness of wave operators for fourth order Schrödinger operators on ^4

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