Hardy’s inequality for the fractional powers of a discrete Laplacian

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.