{
  "abstract": "Given rearrangement-invariant (r.i.) spaces $X$ and $Y$, we show that the segment multiplier, the truncated Hilbert transform, and the discrete Hilbert transform (on the associated discretized space) are bounded from $X$ to $Y$ simultaneously. Moreover, when $X = Y$ this boundedness is characterized by a condition on a pair of Boyd-type indices. We also exhibit an r.i. space on which the segment multiplier is bounded while the (non-truncated) Hilbert transform fails to be bounded.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.22277",
  "author_total": 4,
  "authors": [
    {
      "name": "Miguel F. Barea-Fernández"
    },
    {
      "name": "Ron Kerman"
    },
    {
      "name": "Jan Lang"
    },
    {
      "name": "Javier Soria"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9j5xy8k8hvyjq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.22277",
  "fulltext_url": null,
  "id": "9j5xy8k8hvyjq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.22277",
  "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",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7171373669",
  "pdf_url": "https://arxiv.org/pdf/2607.22277",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9j5xy8k8hvyjq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2607.22277",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.22277"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Characterization of the boundedness of the segment multiplier on rearrangement-invariant spaces",
  "title_text": "Characterization of the boundedness of the segment multiplier on rearrangement-invariant spaces",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/9j5xy8k8hvyjq",
  "venue": "arXiv",
  "versions": []
}