{
  "abstract": "In this paper, we study the behavior of integral kernel operators acting on functions of a single real variable. In particular, we attempt to find possible candidates for their optimal endpoint spaces in the class of Banach spaces endowed with a rearrangement-invariant quasinorm. To achieve this, we characterize the existence of a concrete pointwise estimate for their nonincreasing rearrangement. We also build a theory of optimal endpoint spaces for the Calderón operator given by this pointwise estimate. We use these results to propose optimal endpoint spaces for some integral kernel operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.05070",
  "author_total": 1,
  "authors": [
    {
      "name": "Ivan Kotalík"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9v50q8kasav2d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.05070",
  "fulltext_url": null,
  "id": "9v50q8kasav2d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.05070",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7167608781",
  "pdf_url": "https://arxiv.org/pdf/2607.05070",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9v50q8kasav2d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2607.05070",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.05070"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On optimal endpoints for integral kernel operators",
  "title_text": "On optimal endpoints for integral kernel operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/9v50q8kasav2d",
  "venue": "arXiv",
  "versions": []
}