continuity of wave operators in

We recover for discrete Schrödinger operators on the lattice Z , stronger analogues of the results by Weder [R. Weder, The W k , p continuity of the Schrödinger wave operators on the line, Comm. Math. Phys. 208 (1999) 507–520] and by DʹAncona and Fanelli [P. DʹAncona, L. Fanelli, L p boundedness of the wave operator for the one-dimensional Schrödinger operator, Comm. Math. Phys. 268 (2006) 415–438] on R .