{
  "abstract": "We establish Hardy--Sobolev--Maz'ya inequalities in the subquadratic range $1<p<2$ for singularities supported on affine subspaces and for arbitrary domains. We first prove a Hardy--Sobolev--Maz'ya inequality for singularities supported on affine subspaces of arbitrary codimension $1\\leq k<N$, showing that the deficit in the sharp Hardy inequality controls a suitable weighted Sobolev norm. Combining the same convexity estimate with the one-dimensional approach of Frank and Loss in [9], we also establish Hardy--Sobolev--Maz'ya inequalities on arbitrary domains with the mean distance to the boundary and thereby solve a problem posed in [9]. These results complete the previously unresolved subquadratic range $1<p<2$ and, together with the known results for $p\\geq 2$, provide a unified Hardy--Sobolev--Maz'ya theory for all $1<p<N$ associated with plane singularities and general domains.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22540",
  "author_total": 3,
  "authors": [
    {
      "name": "Avas Banerjee"
    },
    {
      "name": "Michał Kijaczko"
    },
    {
      "name": "Vivek Sahu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cp5hxxn1683vy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22540",
  "fulltext_url": null,
  "id": "cp5hxxn1683vy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22540",
  "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": "W7222971844",
  "pdf_url": "https://arxiv.org/pdf/2610.22540",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cp5hxxn1683vy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.22540",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22540"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Hardy-Sobolev-Maz'ya inequalities for $\\boldsymbol{1<p<2}$",
  "title_text": "Hardy-Sobolev-Maz'ya inequalities for 1<p<2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/cp5hxxn1683vy",
  "venue": "arXiv",
  "versions": []
}