{
  "abstract": "The main purpose of this article is to provide a fractional counterpart of the well-known Maz'ya inequality on the half-space, that is $$ \\int_{\\mathbb{R}^{d}_{+}}\\int_{\\mathbb{R}^{d}_{+}}\\frac{|u(x)-u(y)|^p}{|x-y|^{d+sp}}dy\\,dx\\ge\\mathcal{D}_{d,s,p}\\int_{\\mathbb{R}^{d}_{+}}\\frac{|u(x)|^p}{x_d^{sp}}dx+C_{d,s,p,τ}\\int_{\\mathbb{R}^{d}_{+}}\\frac{|u(x)|^p}{x_{d}^{sp-τ}\\left(x_{d-1}^2+x_d^2\\right)^{τ/2}}dx, $$ where $\\mathcal{D}_{d,s,p}$ stands for the sharp constant in the fractional Hardy inequality on a half-space $\\mathbb{R}^{d}_{+}$. We also obtain a similar result in the setting of Sobolev--Bregman forms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10832",
  "author_total": 2,
  "authors": [
    {
      "name": "Michał Kijaczko"
    },
    {
      "name": "Antoni Szczukiewicz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fce55s2k22z87.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10832",
  "fulltext_url": null,
  "id": "fce55s2k22z87",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10832",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7212247023",
  "pdf_url": "https://arxiv.org/pdf/2609.10832",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fce55s2k22z87.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10832",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10832"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Fractional Hardy--Maz'ya inequality on a half-space",
  "title_text": "Fractional Hardy--Maz'ya inequality on a half-space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/fce55s2k22z87",
  "venue": "arXiv",
  "versions": []
}