Weighted estimates for the Laplacian on the cubic lattice

TY - JOUR

T1 - Weighted estimates for the Laplacian on the cubic lattice

AU - Korotyaev, Evgeny

AU - Møller, Jacob Schach

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Bessel function

KW - Birman-Schwinger

KW - Resolvent

KW - discrete Laplacian

UR - http://www.scopus.com/inward/record.url?scp=85074108166&partnerID=8YFLogxK

U2 - 10.4310/ARKIV.2019.v57.n2.a8

DO - 10.4310/ARKIV.2019.v57.n2.a8

M3 - Journal article

SN - 0004-2080

VL - 57

SP - 397

EP - 428

JO - Arkiv foer Matematik

JF - Arkiv foer Matematik

IS - 2

ER -