Optimal Hardy Inequalities for Fractional $p$-Laplacians on the Integers

Florian Fischer, Marius Nietschmann

We obtain optimal Hardy inequalities for fractional powers of the $p$-Laplacian ${\Delta }_p^{\sigma }$ on $\mathbb{Z}$, $p\in (1,\infty )$, $\sigma \in (0,1/p)$. Asymptotically, the optimal weights beh…