{"paper":{"title":"Hilbert matrix operator on bound analytic functions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Pengcheng Tang, Yuting Guo","submitted_at":"2024-10-24T12:18:58Z","abstract_excerpt":"It is well known that the Hilbert matrix operator $\\mathcal {H}$ is bounded from $H^{\\infty}$ to the mean Lipschitz spaces $\\Lambda^{p}_{\\frac{1}{p}}$ for all $1<p<\\infty$. In this paper, we prove that the range of Hilbert matrix operator $\\mathcal {H}$ acting on $H^{\\infty}$ is contained in certain Zygmund-type space (denoted by $\\Lambda^{1.*}_{1}$), which is strictly smaller than $\\cap_{p>1}\\Lambda^{p}_{\\frac{1}{p}}$. We also provide explicit upper and lower bounds for the norm of the Hilbert matrix $\\mathcal {H}$ acting from $H^{\\infty}$ to $\\Lambda^{1.*}_{1}$. Additionally, we also charact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.18682","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.18682/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}