{
  "abstract": "Let $\\{T_t\\}_{t\\in\\mathbb R}$ be a measure-preserving flow on a probability space $(Ω,Σ,μ)$ and let $T^*$ be the associated one-sided ergodic maximal operator. We show that the sharp Tauberian constant $C(α)=\\sup_{μ(E)>0}\\frac{μ(\\{T^*χ_E>α\\})}{μ(E)}$,$0<α<1$, equals $1/α$ for every $α\\in(0,1)$, unless every measurable set is invariant modulo null sets, in which case $C(α)=1$ for every $α$. In particular the Solyanik estimate $\\lim_{α\\to1^-}C(α)=1$ holds for every measure-preserving flow, and for ergodic flows on nonatomic spaces the estimate $C(α)-1\\le 1/α-1$ holds with equality. This answers the one-parameter case of a question of Hagelstein and Parissis. The main point is the lower bound, which is obtained from a lacunary cross-section built out of the upcrossings of a probe function along the orbits of the flow.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41151",
  "author_total": 1,
  "authors": [
    {
      "name": "Kesen Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/47hqmr39sjtb4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41151",
  "fulltext_url": null,
  "id": "47hqmr39sjtb4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41151",
  "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.DS"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41151",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/47hqmr39sjtb4.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41151",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41151"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Solyanik Estimates for Ergodic Flows",
  "title_text": "Solyanik Estimates for Ergodic Flows",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/47hqmr39sjtb4",
  "venue": "arXiv",
  "versions": []
}