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arXiv · 2609.37336

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

Florian Fischer·Marius Nietschmann
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Abstract

We obtain optimal Hardy inequalities for fractional powers of the $p$-Laplacian $Δ_p^σ$ on $\mathbb{Z}$, $p\in (1,\infty)$, $σ\in (0, 1/p)$. Asymptotically, the optimal weights behave like $|x|^{-pσ}$ as $|x|\to \infty$. We show a similar result for the Riesz fractional $p$-Laplacian. In an appendix, we show that for general $p$-Laplace operators on locally summable graphs, $p$-null-criticality implies $p$-optimality at infinity.

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Florian Fischer, Marius Nietschmann. 2026-09-29. Optimal Hardy Inequalities for Fractional $p$-Laplacians on the Integers. https://arxiv.org/abs/2609.37336

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