Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.37336

Authors: Fischer, Florian, Nietschmann, Marius

Institutions: University of Bonn, Centre National de la Recherche Scientifique, Université Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Université

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214990650

Cites: 35

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Related to: 10