{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:OPIHIHMVTCABO65OJJ6OHY7NG2","short_pith_number":"pith:OPIHIHMV","schema_version":"1.0","canonical_sha256":"73d0741d959880177bae4a7ce3e3ed36bf8059be5fb71bad9b38eb0d0182a805","source":{"kind":"arxiv","id":"1805.07804","version":1},"attestation_state":"computed","paper":{"title":"Norm estimates of weighted composition operators pertaining to the Hilbert Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mikael Lindstr\\\"om, Niklas Wikman, Santeri Miihkinen","submitted_at":"2018-05-20T17:43:32Z","abstract_excerpt":"Very recently, Bo\\v{z}in and Karapetrovi\\'c solved a conjecture by proving that the norm of the Hilbert matrix operator $\\mathcal{H}$ on the Bergman space $A^p$ is equal to $\\frac{\\pi}{\\sin(\\frac{2\\pi}{p})}$ for $2 < p < 4.$ In this article we present a partly new and simplified proof of this result. Moreover, we calculate the exact value of the norm of $\\mathcal{H}$ defined on the Korenblum spaces $H^\\infty_\\alpha$ for $0 < \\alpha \\le 2/3$ and an upper bound for the norm on the scale $2/3 < \\alpha < 1$."},"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":"1805.07804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-20T17:43:32Z","cross_cats_sorted":[],"title_canon_sha256":"97d8599f9c21b9aaaea8764f4ab90d70687ccc33c870281dfdec07c33b05e7b3","abstract_canon_sha256":"583853ad53bd1d40509caea70a161a549367d79e6f105ff041a44349b7ee82e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:32.498629Z","signature_b64":"/+UfbSXg4U5pdw3nm0hwGTjRDP1dYen4rnbfjulqSzgx4GgLphOH4Fg4Mj6DPFT/PrbJxXQqUEG+sdtkauQOBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73d0741d959880177bae4a7ce3e3ed36bf8059be5fb71bad9b38eb0d0182a805","last_reissued_at":"2026-05-18T00:15:32.498026Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:32.498026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Norm estimates of weighted composition operators pertaining to the Hilbert Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mikael Lindstr\\\"om, Niklas Wikman, Santeri Miihkinen","submitted_at":"2018-05-20T17:43:32Z","abstract_excerpt":"Very recently, Bo\\v{z}in and Karapetrovi\\'c solved a conjecture by proving that the norm of the Hilbert matrix operator $\\mathcal{H}$ on the Bergman space $A^p$ is equal to $\\frac{\\pi}{\\sin(\\frac{2\\pi}{p})}$ for $2 < p < 4.$ In this article we present a partly new and simplified proof of this result. Moreover, we calculate the exact value of the norm of $\\mathcal{H}$ defined on the Korenblum spaces $H^\\infty_\\alpha$ for $0 < \\alpha \\le 2/3$ and an upper bound for the norm on the scale $2/3 < \\alpha < 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07804","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":"1805.07804","created_at":"2026-05-18T00:15:32.498129+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.07804v1","created_at":"2026-05-18T00:15:32.498129+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07804","created_at":"2026-05-18T00:15:32.498129+00:00"},{"alias_kind":"pith_short_12","alias_value":"OPIHIHMVTCAB","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"OPIHIHMVTCABO65O","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"OPIHIHMV","created_at":"2026-05-18T12:32:43.782077+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/OPIHIHMVTCABO65OJJ6OHY7NG2","json":"https://pith.science/pith/OPIHIHMVTCABO65OJJ6OHY7NG2.json","graph_json":"https://pith.science/api/pith-number/OPIHIHMVTCABO65OJJ6OHY7NG2/graph.json","events_json":"https://pith.science/api/pith-number/OPIHIHMVTCABO65OJJ6OHY7NG2/events.json","paper":"https://pith.science/paper/OPIHIHMV"},"agent_actions":{"view_html":"https://pith.science/pith/OPIHIHMVTCABO65OJJ6OHY7NG2","download_json":"https://pith.science/pith/OPIHIHMVTCABO65OJJ6OHY7NG2.json","view_paper":"https://pith.science/paper/OPIHIHMV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.07804&json=true","fetch_graph":"https://pith.science/api/pith-number/OPIHIHMVTCABO65OJJ6OHY7NG2/graph.json","fetch_events":"https://pith.science/api/pith-number/OPIHIHMVTCABO65OJJ6OHY7NG2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OPIHIHMVTCABO65OJJ6OHY7NG2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OPIHIHMVTCABO65OJJ6OHY7NG2/action/storage_attestation","attest_author":"https://pith.science/pith/OPIHIHMVTCABO65OJJ6OHY7NG2/action/author_attestation","sign_citation":"https://pith.science/pith/OPIHIHMVTCABO65OJJ6OHY7NG2/action/citation_signature","submit_replication":"https://pith.science/pith/OPIHIHMVTCABO65OJJ6OHY7NG2/action/replication_record"}},"created_at":"2026-05-18T00:15:32.498129+00:00","updated_at":"2026-05-18T00:15:32.498129+00:00"}