{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37336",
  "author_total": 2,
  "authors": [
    {
      "name": "Florian Fischer"
    },
    {
      "name": "Marius Nietschmann"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2wn1tx2rjp3wj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37336",
  "fulltext_url": null,
  "id": "2wn1tx2rjp3wj",
  "issns": [],
  "landing_url": "https://hal.science/hal-05779464v1",
  "language": "en",
  "licence": "LicenseRef-publisher-terms",
  "licence_label": "Publisher terms",
  "licence_source": "article",
  "licence_url": "https://hal.science/licences/copyright/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7214990650",
  "pdf_url": "https://hal.science/hal-05779464/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2wn1tx2rjp3wj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "hal-05779464",
      "source": "hal",
      "url": "https://hal.science/hal-05779464v1"
    },
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.37336",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37336"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Optimal Hardy Inequalities for Fractional $p$-Laplacians on the Integers",
  "title_text": "Optimal Hardy Inequalities for Fractional p-Laplacians on the Integers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/2wn1tx2rjp3wj",
  "venue": "HAL",
  "versions": []
}