{
  "abstract": "For $d\\geq2$, $0<s<1$, $p>1$, and $τ>0$, we study the sharp half-space remainder \\[ [u]_{s,p,+}^p-\\mathcal D_{d,s,p}\\int_{\\mathbb R^d_+}x_d^{-sp}|u|^p\\,dx \\geqΛ_{d,s,p,τ}\\int_{\\mathbb R^d_+} \\frac{x_d^{τ-sp}|u|^p}{(x_{d-1}^2+x_d^2)^{τ/2}}\\,dx. \\] We first obtain exact dimensional and angular reductions by an $L^p$ contraction. For $p=2$, we identify the planar sharp coefficient with the simple first eigenvalue of a singular angular operator with compact resolvent. We prove a ground-state representation and a two-sided estimate for the sharp deficit. These give quantitative stability and a Fourier--Mellin energy criterion for extremizing sequences in all dimensions. For the distance with multiplier $h(ξ)=\\min\\{ξ^2,1\\}$, the best planar stability coefficient is not attained and is strictly smaller than the quadratic dispersion coefficient. The minimizing frequencies are nonzero when $τ=2$ and $s$ is close to one. Finally, we prove normalized local limits for the sharp quadratic constant, each fixed fiber eigenvalue, and the dispersion coefficient.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31595",
  "author_total": 2,
  "authors": [
    {
      "name": "Shengbing Deng"
    },
    {
      "name": "Dehong Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/88vybhj4jd0nq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31595",
  "fulltext_url": null,
  "id": "88vybhj4jd0nq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31595",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7223414636",
  "pdf_url": "https://arxiv.org/pdf/2610.31595",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/88vybhj4jd0nq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31595",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31595"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp fractional Hardy--Maz'ya remainders on half-spaces: angular reduction and energy stability",
  "title_text": "Sharp fractional Hardy--Maz'ya remainders on half-spaces: angular reduction and energy stability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/88vybhj4jd0nq",
  "venue": "arXiv",
  "versions": []
}