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Статья

Weighted estimates for the Laplacian on the cubic lattice

Arkiv for Matematik. 2019. Vol. 57. No. 2. P. 397-428.
Evgeny L. Korotyaev, Moller J.

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.