{
  "abstract": "We study compactness of the product of two weighted Hardy primitives into $L^q(u)$, $0<q<\\infty$, on the input boundary $1\\le p_1,p_2\\le\\infty$, where at least one input exponent is $1$ or $\\infty$. For $L^1\\times L^p$, $1<p<\\infty$, boundedness implies compactness when $q<p/(p+1)$. For $L^1\\times L^1$, the corresponding range is $q<1/2$. At and above these boundaries compactness is characterized by additional active-tail decay, and critical power weights give bounded noncompact examples. The endpoint reductions use cumulative Stieltjes measures with their initial atoms and strict Hardy-Copson brackets. An output-mass allocation argument proves local finite-rank density, including quasi-Banach targets. Applying the localization principles developed for the interior-input regime identifies the essential distance, finite-rank distance and Hausdorff noncompactness radius with the coupled active tail, with the appropriate metric power when $q<1$. For a finite left endpoint, ordinary $L^\\infty$ inputs admit an exact scalar transfer completed by linear nodal approximation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02649",
  "author_total": 1,
  "authors": [
    {
      "name": "Saikat Kanjilal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5xggcgcp4dvtr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02649",
  "fulltext_url": null,
  "id": "5xggcgcp4dvtr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02649",
  "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.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.02649",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5xggcgcp4dvtr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02649",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02649"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Input-Endpoint Compactness and Essential Norms for Weighted Bilinear Hardy Operators",
  "title_text": "Input-Endpoint Compactness and Essential Norms for Weighted Bilinear Hardy Operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/5xggcgcp4dvtr",
  "venue": "arXiv",
  "versions": []
}