Weighted estimates for the Laplacian on the cubic lattice

Abstract

We consider the discrete Laplacian Δ on the cubic lattice Zd, and deduce estimates on the group eitΔ and the resolvent (Δ−z)−1, weighted by q(Zd)-weights for suitable q 2. We apply the obtained results to discrete Schrödinger operators in dimension d 3 with potentials from p(Zd) with suitable p 1.