{
  "abstract": "For $1<q<p<\\infty$ we study the $L^p\\to L^q$ contractivity of the two-point operator $T_ω(a+bx)=a+ωbx$ with a complex parameter $ω$, extending the Weissler two-point condition, usually discussed in the range $1<p\\le q<\\infty$, to the reversed order of exponents. For $1<q<p<2$ we prove that the second-order necessary condition $|(p-2)-(q-2)ω^2|\\le p-q|ω|^2$, obtained near $(a,b)=(1,0)$, is also sufficient; by duality the same description applies to $2<q<p<\\infty$. The proof uses the method of characteristic flows. In addition, for $q\\le2\\le p$ the contractivity follows directly from $L^2$ contraction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00835",
  "author_total": 1,
  "authors": [
    {
      "name": "Di Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8ahk1hj8ppw4t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00835",
  "fulltext_url": null,
  "id": "8ahk1hj8ppw4t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00835",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00835",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8ahk1hj8ppw4t.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00835",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00835"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Two-Point Inequality for $p>q$",
  "title_text": "The Two-Point Inequality for p>q",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/8ahk1hj8ppw4t",
  "venue": "arXiv",
  "versions": []
}