Weighted estimates for the Laplacian on the cubic lattice

Evgeny Korotyaev, Jacob Schach Møller

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Abstract

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

OriginalsprogEngelsk
TidsskriftArkiv foer Matematik
Vol/bind57
Nummer2
Sider (fra-til)397-428
Antal sider32
ISSN0004-2080
DOI
StatusUdgivet - 2019

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