{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:P2JCLQOHWLK6KDKHN4UHTZCRRA","short_pith_number":"pith:P2JCLQOH","canonical_record":{"source":{"id":"1805.11967","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-05-30T13:53:51Z","cross_cats_sorted":[],"title_canon_sha256":"8ba254731ccf546980e21606b4d13217b773b163e62881ea23e44e2f0bafbe28","abstract_canon_sha256":"b39c1651c60d0902751b77a509051d77b699a031f5e810130585347bf4b17939"},"schema_version":"1.0"},"canonical_sha256":"7e9225c1c7b2d5e50d476f2879e451882e37e2eb67bc88cc84a916845db102f0","source":{"kind":"arxiv","id":"1805.11967","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11967","created_at":"2026-05-18T00:14:35Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11967v1","created_at":"2026-05-18T00:14:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11967","created_at":"2026-05-18T00:14:35Z"},{"alias_kind":"pith_short_12","alias_value":"P2JCLQOHWLK6","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P2JCLQOHWLK6KDKH","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P2JCLQOH","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:P2JCLQOHWLK6KDKHN4UHTZCRRA","target":"record","payload":{"canonical_record":{"source":{"id":"1805.11967","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-05-30T13:53:51Z","cross_cats_sorted":[],"title_canon_sha256":"8ba254731ccf546980e21606b4d13217b773b163e62881ea23e44e2f0bafbe28","abstract_canon_sha256":"b39c1651c60d0902751b77a509051d77b699a031f5e810130585347bf4b17939"},"schema_version":"1.0"},"canonical_sha256":"7e9225c1c7b2d5e50d476f2879e451882e37e2eb67bc88cc84a916845db102f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:35.623465Z","signature_b64":"vpfkwvA0ioQHFOUs5wGSTNpMMhNFtbkE8kodmnqOBvjb7fcqFAIcexZXFw24EjI+2ktK+I1ObUrFEaIW2AckDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e9225c1c7b2d5e50d476f2879e451882e37e2eb67bc88cc84a916845db102f0","last_reissued_at":"2026-05-18T00:14:35.622939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:35.622939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.11967","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bVcfcXNEIRpfa+ZpMph45iTI+a3eB5rbMk+YjYnIJuZRbg7J20IrNeOHncv8Dy0xWUTrE4njPnfh+O6ZUPWIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:15:18.221866Z"},"content_sha256":"60d684b615f80099d572822b560a716fbda2ac5f857c51ab7a347028e228474f","schema_version":"1.0","event_id":"sha256:60d684b615f80099d572822b560a716fbda2ac5f857c51ab7a347028e228474f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:P2JCLQOHWLK6KDKHN4UHTZCRRA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Essential norm of generalized Hilbert matrix from Bloch type spaces to BMOA and Bloch space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jizhen Zhou, Songxiao Li","submitted_at":"2018-05-30T13:53:51Z","abstract_excerpt":"Let $\\mu$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\\mathcal{H}_\\mu=(\\mu_{n+k})_{n,k\\geq 0}$ with entries $\\mu_{n,k}=\\mu_{n+k}$ induces the operator $$ \\mathcal{H}_\\mu(f)(z)=\\sum^\\infty_{n=0}\\left(\\sum^\\infty_{k=0}\\mu_{n,k}a_k\\right)z^n $$ on the space of all analytic functions $f(z)=\\sum^\\infty_{n=0}a_nz^n$ in the unit disk $\\mathbb{D}$. In this paper, we characterize the boundedness and compactness of $\\mathcal{H}_\\mu$ from Bloch type spaces to the BMOA and the Bloch space. Moreover we obtain the essential norm of $\\mathcal{H}_\\mu$ from $\\alpha$ Bloch type space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11967","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y7mAqkZT4nboBj4r0ZjVjO887SzXpZBYLVq14icaTv9qnCzOx2nuqgFreaHd2iJBmOSQOPyA2bmWcloEY9gdDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:15:18.222607Z"},"content_sha256":"f9ae10adaa4c229b09f562e9ac6958bc4819e74bf1105154a4ad52c6a971532c","schema_version":"1.0","event_id":"sha256:f9ae10adaa4c229b09f562e9ac6958bc4819e74bf1105154a4ad52c6a971532c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P2JCLQOHWLK6KDKHN4UHTZCRRA/bundle.json","state_url":"https://pith.science/pith/P2JCLQOHWLK6KDKHN4UHTZCRRA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P2JCLQOHWLK6KDKHN4UHTZCRRA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T11:15:18Z","links":{"resolver":"https://pith.science/pith/P2JCLQOHWLK6KDKHN4UHTZCRRA","bundle":"https://pith.science/pith/P2JCLQOHWLK6KDKHN4UHTZCRRA/bundle.json","state":"https://pith.science/pith/P2JCLQOHWLK6KDKHN4UHTZCRRA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P2JCLQOHWLK6KDKHN4UHTZCRRA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:P2JCLQOHWLK6KDKHN4UHTZCRRA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b39c1651c60d0902751b77a509051d77b699a031f5e810130585347bf4b17939","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-05-30T13:53:51Z","title_canon_sha256":"8ba254731ccf546980e21606b4d13217b773b163e62881ea23e44e2f0bafbe28"},"schema_version":"1.0","source":{"id":"1805.11967","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11967","created_at":"2026-05-18T00:14:35Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11967v1","created_at":"2026-05-18T00:14:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11967","created_at":"2026-05-18T00:14:35Z"},{"alias_kind":"pith_short_12","alias_value":"P2JCLQOHWLK6","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P2JCLQOHWLK6KDKH","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P2JCLQOH","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:f9ae10adaa4c229b09f562e9ac6958bc4819e74bf1105154a4ad52c6a971532c","target":"graph","created_at":"2026-05-18T00:14:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $\\mu$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\\mathcal{H}_\\mu=(\\mu_{n+k})_{n,k\\geq 0}$ with entries $\\mu_{n,k}=\\mu_{n+k}$ induces the operator $$ \\mathcal{H}_\\mu(f)(z)=\\sum^\\infty_{n=0}\\left(\\sum^\\infty_{k=0}\\mu_{n,k}a_k\\right)z^n $$ on the space of all analytic functions $f(z)=\\sum^\\infty_{n=0}a_nz^n$ in the unit disk $\\mathbb{D}$. In this paper, we characterize the boundedness and compactness of $\\mathcal{H}_\\mu$ from Bloch type spaces to the BMOA and the Bloch space. Moreover we obtain the essential norm of $\\mathcal{H}_\\mu$ from $\\alpha$ Bloch type space","authors_text":"Jizhen Zhou, Songxiao Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-05-30T13:53:51Z","title":"Essential norm of generalized Hilbert matrix from Bloch type spaces to BMOA and Bloch space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11967","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:60d684b615f80099d572822b560a716fbda2ac5f857c51ab7a347028e228474f","target":"record","created_at":"2026-05-18T00:14:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b39c1651c60d0902751b77a509051d77b699a031f5e810130585347bf4b17939","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-05-30T13:53:51Z","title_canon_sha256":"8ba254731ccf546980e21606b4d13217b773b163e62881ea23e44e2f0bafbe28"},"schema_version":"1.0","source":{"id":"1805.11967","kind":"arxiv","version":1}},"canonical_sha256":"7e9225c1c7b2d5e50d476f2879e451882e37e2eb67bc88cc84a916845db102f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e9225c1c7b2d5e50d476f2879e451882e37e2eb67bc88cc84a916845db102f0","first_computed_at":"2026-05-18T00:14:35.622939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:35.622939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vpfkwvA0ioQHFOUs5wGSTNpMMhNFtbkE8kodmnqOBvjb7fcqFAIcexZXFw24EjI+2ktK+I1ObUrFEaIW2AckDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:35.623465Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.11967","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60d684b615f80099d572822b560a716fbda2ac5f857c51ab7a347028e228474f","sha256:f9ae10adaa4c229b09f562e9ac6958bc4819e74bf1105154a4ad52c6a971532c"],"state_sha256":"c13832490de8f2aeb1b4630c1de36c5f5d4421356d78d224743354b876112810"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jeO/yyxX6WEjAXdu5uqlMrritJz7PCEewKkb9fp0RbYw7pFZ8sn7sWtBwyYA9MOprQcy7Gv9acwI2qDidOJBBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T11:15:18.226752Z","bundle_sha256":"91539a4334cda00bb25f30eaefce16352ffc2361ecd2a6077752ef239e4320df"}}