In this paper we consider the wave operators WΒ±β for a Schr\"odinger
operator H in Rn with nβ₯4 even and we discuss the Lp
boundedness of WΒ±β assuming a suitable decay at infinity of the potential
V. The analysis heavily depends on the singularities of the resolvent for
small energy, that is if 0-energy eigenstates exist. If such eigenstates do not
exist WΒ±β:LpβLp are bounded for 1β€pβ€β otherwise
this is true for nβ2nβ<p<2nβ. The extension to Sobolev
space is discussed.Comment: 59 page