{
  "abstract": "A sequence \\((λ_n)_{n\\ge1}\\) of distinct positive integers is called an \\(L^p\\)-Khinchin sequence, where $1\\le p\\le\\infty$, if $ n^{-1}\\sum_{k=1}^n f(λ_k x) \\longrightarrow \\int_{\\mathbb T}f\\,d\\mathfrak m $ a.e. $x\\in\\mathbb T$ for every \\(f\\in L^p(\\mathbb T)\\). When $1\\le p<\\infty$, we characterize the \\(L^p\\)-Khinchin sequences by a weak $(p,p)$ maximal inequality for the associated averaging operators. We also establish a transference principle reducing the weak $(p,p)$ maximal inequality to weak $(p,p)$ maximal inequalities for three model systems: translation along a lattice path in the infinite direct sum of the semigroup $\\mathbb{N}_0$, translation along a lattice path in the infinite direct sum of the group $\\mathbb{Z}$ and translation on the circle $\\mathbb{T}$. As consequences, we prove that $(2^n+1)_{n\\ge1}$, the Fibonacci sequence, sequences of distinct primes and their partial products are \\emph{not} $L^p$-Khinchin for any $1\\le p<\\infty$. We study the special class of multiplicative sequences generated by infinite words and we show that balanced infinite words generate $L^1$-Khinchin sequences, while typical random multiplicative sequences over at least two coprime integers are almost surely not $L^p$-Khinchin for any $1\\le p<\\infty$. We also obtain a {Conze-type principle} for countably generated semigroup actions on a probability space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26152",
  "author_total": 3,
  "authors": [
    {
      "name": "Aihua Fan"
    },
    {
      "name": "Shilei Fan"
    },
    {
      "name": "Tongjin Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d33xgn5gzxsqq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26152",
  "fulltext_url": null,
  "id": "d33xgn5gzxsqq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26152",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7223043656",
  "pdf_url": "https://arxiv.org/pdf/2610.26152",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d33xgn5gzxsqq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26152",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26152"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "$L^p$-Khinchin sequences and transference principles",
  "title_text": "L^p-Khinchin sequences and transference principles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/d33xgn5gzxsqq",
  "venue": "arXiv",
  "versions": []
}