{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:DGNLLVMJE4E5OVK6UOBXLNIKFH","short_pith_number":"pith:DGNLLVMJ","schema_version":"1.0","canonical_sha256":"199ab5d5892709d7555ea38375b50a29e5995ec6c17b6bcd92bc17b2323fdec3","source":{"kind":"arxiv","id":"1309.6125","version":1},"attestation_state":"computed","paper":{"title":"A generalized Hilbert matrix acting on Hardy spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Christos Chatzifountas, Daniel Girela, Jose Angel Pelaez","submitted_at":"2013-09-24T12:08:11Z","abstract_excerpt":"If $\\mu $ is a positive Borel measure on the interval $[0, 1)$, the Hankel matrix $\\mathcal H_\\mu =(\\mu_{n,k})_{n,k\\ge 0}$ with entries $\\mu_{n,k}=\\int_{[0,1)}t^{n+k}\\,d\\mu(t)$ induces formally the operator $$\\mathcal{H}_\\mu (f)(z)=\\sum_{n=0}^{\\infty}\\left(\\sum_{k=0}^{\\infty}\\mu_{n,k}{a_k}\\right)z^n$$ on the space of all analytic functions $f(z)=\\sum_{k=0}^\\infty a_kz^k$, in the unit disc $\\mathbb{D} $. In this paper we describe those measures $\\mu$ for which $\\mathcal{H}_\\mu $ is a bounded (compact) operator from $H^p$ into $H^q$, $0<p,q<\\infty $. We also characterize the measures $\\mu $ for "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1309.6125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-24T12:08:11Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"2d274f2fb54e42d7daa23eef90e0591e5ba329f69ea1c39b55ed37d2761c6d4c","abstract_canon_sha256":"9bfb5e87924ef48cf80e7fe462a74c07d9e896e758e52b6f36a29211829501b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:23.833596Z","signature_b64":"d/BM/ewHSvbdEMYvP8WcOtL41PrAetnSWoGYopn1CuFslhyRhUrbmGN8JGlICVYOZkixRFMm8o1luqzOyhe2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"199ab5d5892709d7555ea38375b50a29e5995ec6c17b6bcd92bc17b2323fdec3","last_reissued_at":"2026-05-18T03:12:23.832816Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:23.832816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A generalized Hilbert matrix acting on Hardy spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Christos Chatzifountas, Daniel Girela, Jose Angel Pelaez","submitted_at":"2013-09-24T12:08:11Z","abstract_excerpt":"If $\\mu $ is a positive Borel measure on the interval $[0, 1)$, the Hankel matrix $\\mathcal H_\\mu =(\\mu_{n,k})_{n,k\\ge 0}$ with entries $\\mu_{n,k}=\\int_{[0,1)}t^{n+k}\\,d\\mu(t)$ induces formally the operator $$\\mathcal{H}_\\mu (f)(z)=\\sum_{n=0}^{\\infty}\\left(\\sum_{k=0}^{\\infty}\\mu_{n,k}{a_k}\\right)z^n$$ on the space of all analytic functions $f(z)=\\sum_{k=0}^\\infty a_kz^k$, in the unit disc $\\mathbb{D} $. In this paper we describe those measures $\\mu$ for which $\\mathcal{H}_\\mu $ is a bounded (compact) operator from $H^p$ into $H^q$, $0<p,q<\\infty $. We also characterize the measures $\\mu $ for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6125","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1309.6125","created_at":"2026-05-18T03:12:23.832920+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.6125v1","created_at":"2026-05-18T03:12:23.832920+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6125","created_at":"2026-05-18T03:12:23.832920+00:00"},{"alias_kind":"pith_short_12","alias_value":"DGNLLVMJE4E5","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"DGNLLVMJE4E5OVK6","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"DGNLLVMJ","created_at":"2026-05-18T12:27:43.054852+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DGNLLVMJE4E5OVK6UOBXLNIKFH","json":"https://pith.science/pith/DGNLLVMJE4E5OVK6UOBXLNIKFH.json","graph_json":"https://pith.science/api/pith-number/DGNLLVMJE4E5OVK6UOBXLNIKFH/graph.json","events_json":"https://pith.science/api/pith-number/DGNLLVMJE4E5OVK6UOBXLNIKFH/events.json","paper":"https://pith.science/paper/DGNLLVMJ"},"agent_actions":{"view_html":"https://pith.science/pith/DGNLLVMJE4E5OVK6UOBXLNIKFH","download_json":"https://pith.science/pith/DGNLLVMJE4E5OVK6UOBXLNIKFH.json","view_paper":"https://pith.science/paper/DGNLLVMJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.6125&json=true","fetch_graph":"https://pith.science/api/pith-number/DGNLLVMJE4E5OVK6UOBXLNIKFH/graph.json","fetch_events":"https://pith.science/api/pith-number/DGNLLVMJE4E5OVK6UOBXLNIKFH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DGNLLVMJE4E5OVK6UOBXLNIKFH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DGNLLVMJE4E5OVK6UOBXLNIKFH/action/storage_attestation","attest_author":"https://pith.science/pith/DGNLLVMJE4E5OVK6UOBXLNIKFH/action/author_attestation","sign_citation":"https://pith.science/pith/DGNLLVMJE4E5OVK6UOBXLNIKFH/action/citation_signature","submit_replication":"https://pith.science/pith/DGNLLVMJE4E5OVK6UOBXLNIKFH/action/replication_record"}},"created_at":"2026-05-18T03:12:23.832920+00:00","updated_at":"2026-05-18T03:12:23.832920+00:00"}