{
  "abstract": "Let $-A$ be the generator of a real, symmetric contraction semigroup on a $σ$-finite measure space. We prove a universal bound for maximal $\\mathrm{L}^p$-regularity: In space-time norms $$\\|Au\\|_p \\leq \\big(p^* + \\tfrac{p^*}{2(p^*-1)}\\big) \\|f\\|_p,$$ where $p^* = \\max(p,p/(p-1))$ and $u$ is the mild solution to the Cauchy problem with right-hand side $f$ starting at $u(0)=0$. Linear growth of the constant in $p^*$ is optimal. Our proof introduces an elementary approach to maximal regularity that avoids both vector-valued harmonic analysis and dilation theory. We also obtain quantitative maximal regularity estimates for real, non-symmetric semigroups that are contractive on a sector.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23357",
  "author_total": 3,
  "authors": [
    {
      "name": "Moritz Egert"
    },
    {
      "name": "Jan Giesselmann"
    },
    {
      "name": "Marc Hoffmann"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/330jjsdt48sz4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23357",
  "fulltext_url": null,
  "id": "330jjsdt48sz4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23357",
  "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",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7222938078",
  "pdf_url": "https://arxiv.org/pdf/2610.23357",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/330jjsdt48sz4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23357",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23357"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Quantitative maximal $\\mathrm{L}^p$-regularity for generators of real contraction semigroups",
  "title_text": "Quantitative maximal L^p-regularity for generators of real contraction semigroups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/330jjsdt48sz4",
  "venue": "arXiv",
  "versions": []
}