{
  "abstract": "We study weighted coefficient estimates for the Laguerre transform in terms of moduli of smoothness generated by the Laguerre translation. For every integer $r\\ge1$ and $1\\le p\\le2$, a weighted $\\ell^{p'}$ norm of $\\min\\{1,nt\\}^{r}\\widehat f_α(n)$ is bounded by the modulus of order $r$; for $2\\le p\\le\\infty$ the reverse direction holds on the same weighted sequence scale. At $p=2$ these estimates yield a two-sided equivalence, and testing individual Laguerre polynomials proves optimality of the multiplier weight up to constants. The proof combines Hausdorff--Young inequalities with an averaged lower bound for the translation multiplier. As consequences we recover Jackson- and Bernstein-type estimates and the known $L^2$ approximation characterisation of the Lipschitz classes for $0<β<r$. We also give the corresponding one-sided coefficient-tail criteria for general $p$, together with saturation and endpoint statements.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08167",
  "author_total": 2,
  "authors": [
    {
      "name": "Nurbek Kakharman"
    },
    {
      "name": "Niyaz Tokmagambetov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e0fbj7qm9jydd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08167",
  "fulltext_url": null,
  "id": "e0fbj7qm9jydd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08167",
  "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",
      "2613|Approximation Theory and Sequence Spaces"
    ]
  ],
  "openalex": "W7221051684",
  "pdf_url": "https://arxiv.org/pdf/2610.08167",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e0fbj7qm9jydd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08167",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08167"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Moduli of smoothness and growth of the Laguerre transform: two-sided estimates",
  "title_text": "Moduli of smoothness and growth of the Laguerre transform: two-sided estimates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/e0fbj7qm9jydd",
  "venue": "arXiv",
  "versions": []
}