Optimal Hardy weights for the fractional discrete Dirichlet Laplacian on the half-line

František Štampach, Jakub Waclawek

For positive powers of the discrete Dirichlet Laplacian $(-{\Delta }_{\mathrm{D}}{)}^{\sigma }$, non-trivial Hardy weights exist if and only if $0<\sigma <3/2$. For $0<\sigma \le 1$, an explicit optimal Hardy…