Abstract
We prove a Hardy inequality for fractional powers of a discrete Laplacian, which can be seen as a generalized fractional version of the classical Hardy inequality in Landau (J Lond Math Soc 1:38–39, 1926). Such inequality will be deduced from a ground state representation, following in this way the approach used by Frank, Lieb, and Seiringer in the continuous Euclidean setting.
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