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October 2019 Weighted estimates for the Laplacian on the cubic lattice
Evgeny L. Korotyaev, Jacob Schach Møller
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Ark. Mat. 57(2): 397-428 (October 2019). DOI: 10.4310/ARKIV.2019.v57.n2.a8

Abstract

We consider the discrete Laplacian $\Delta$ on the cubic lattice $\mathbb{Z}^d$, and deduce estimates on the group $e^{i t \Delta}$ and the resolvent $(\Delta-z)^{-1}$, weighted by $\ell^q (\mathbb{Z}^d)$-weights for suitable $q \geqslant 2$. We apply the obtained results to discrete Schrödinger operators in dimension $d \geqslant 3$ with potentials from $\ell^p (\mathbb{Z}^d)$ with suitable $p \geqslant1$.

Funding Statement

The authors were supported by the RSF grant No 18-11-00032, and by the Danish Council for Independent Research grant No 1323-00360.

Citation

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Evgeny L. Korotyaev. Jacob Schach Møller. "Weighted estimates for the Laplacian on the cubic lattice." Ark. Mat. 57 (2) 397 - 428, October 2019. https://doi.org/10.4310/ARKIV.2019.v57.n2.a8

Information

Received: 6 November 2018; Published: October 2019
First available in Project Euclid: 16 April 2020

zbMATH: 1427.47014
MathSciNet: MR4018760
Digital Object Identifier: 10.4310/ARKIV.2019.v57.n2.a8

Subjects:
Primary: 33C10, 47A40, 81Q10, 81Q35

Rights: Copyright © 2019 Institut Mittag-Leffler

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Vol.57 • No. 2 • October 2019
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