{"paper":{"title":"Generalized Hilbert operators on Hardy spaces","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pengcheng Tang, Yuting Guo","submitted_at":"2026-07-30T13:56:39Z","abstract_excerpt":"Let $g\\in H(\\mathbb D)$, the generalized Hilbert operator $\\mathcal H_g$ is defined by \\[ \\mathcal H_g(f)(z)=\\int_0^1 f(t)g'(tz)dt,\\ \\ z\\in \\mathbb D\\, \\ \\ f \\in H(\\mathbb D). \\] Let $\\mathcal R_p=\\mathcal H(H^p)$ be the range of the classical Hilbert operator on Hardy space, equipped with the pullback norm, and let $(\\mathcal R_p,H^p)$ denote the Hadamard multiplier space. For $1<p<\\infty$, we prove the exact multiplier characterization \\[ \\mathcal H_g:H^{p}\\longrightarrow H^{p} \\ \\ \\text{is bounded} \\quad\\Longleftrightarrow\\quad g'\\in(\\mathcal R_p,H^p), \\] and an equivalent Hilbert-matrix bi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28221","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/2607.28221/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"}