{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YSHHV3W5CQWNI2WY63QFBJIPCU","short_pith_number":"pith:YSHHV3W5","schema_version":"1.0","canonical_sha256":"c48e7aeedd142cd46ad8f6e050a50f1522c5e291e5b9ee746fc2ec412782752e","source":{"kind":"arxiv","id":"1406.1299","version":1},"attestation_state":"computed","paper":{"title":"Analytic version of critical $Q$ spaces and their properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Junming Liu, Pengtao Li, Zengjian Lou","submitted_at":"2014-06-05T08:56:05Z","abstract_excerpt":"In this paper, we establish an analytic version of critical spaces $Q_{\\alpha}^{\\beta}(\\mathbb{R}^{n})$ on unit disc $\\mathbb{D}$, denoted by $Q^{\\beta}_{p}(\\mathbb{D})$. Further we prove a relation between $Q^{\\beta}_{p}(\\mathbb{D})$ and Morrey spaces. By the boundedness of two integral operators, we give the multiplier spaces of $Q^{\\beta}_{p}(\\mathbb{D})$."},"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":"1406.1299","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-05T08:56:05Z","cross_cats_sorted":[],"title_canon_sha256":"153b43439b6a81094a2f9462644d8665d9dfb0832f74055c2a59a91d3082dd5a","abstract_canon_sha256":"49d321c27ef680bb3f87f5256ca8dc1e171f562926b5bb919f32122a1e5c34a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:23.557934Z","signature_b64":"rocrejn9WFp/EsCt+WV9UOjtKImesmW3ocHkziDVJ6ywsvC5ImKm4vOKu4K2/1LxzY9fM2sg+4RkYektqTiaBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c48e7aeedd142cd46ad8f6e050a50f1522c5e291e5b9ee746fc2ec412782752e","last_reissued_at":"2026-05-18T02:50:23.557401Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:23.557401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytic version of critical $Q$ spaces and their properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Junming Liu, Pengtao Li, Zengjian Lou","submitted_at":"2014-06-05T08:56:05Z","abstract_excerpt":"In this paper, we establish an analytic version of critical spaces $Q_{\\alpha}^{\\beta}(\\mathbb{R}^{n})$ on unit disc $\\mathbb{D}$, denoted by $Q^{\\beta}_{p}(\\mathbb{D})$. Further we prove a relation between $Q^{\\beta}_{p}(\\mathbb{D})$ and Morrey spaces. By the boundedness of two integral operators, we give the multiplier spaces of $Q^{\\beta}_{p}(\\mathbb{D})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1299","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":"1406.1299","created_at":"2026-05-18T02:50:23.557456+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.1299v1","created_at":"2026-05-18T02:50:23.557456+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1299","created_at":"2026-05-18T02:50:23.557456+00:00"},{"alias_kind":"pith_short_12","alias_value":"YSHHV3W5CQWN","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"YSHHV3W5CQWNI2WY","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"YSHHV3W5","created_at":"2026-05-18T12:28:57.508820+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/YSHHV3W5CQWNI2WY63QFBJIPCU","json":"https://pith.science/pith/YSHHV3W5CQWNI2WY63QFBJIPCU.json","graph_json":"https://pith.science/api/pith-number/YSHHV3W5CQWNI2WY63QFBJIPCU/graph.json","events_json":"https://pith.science/api/pith-number/YSHHV3W5CQWNI2WY63QFBJIPCU/events.json","paper":"https://pith.science/paper/YSHHV3W5"},"agent_actions":{"view_html":"https://pith.science/pith/YSHHV3W5CQWNI2WY63QFBJIPCU","download_json":"https://pith.science/pith/YSHHV3W5CQWNI2WY63QFBJIPCU.json","view_paper":"https://pith.science/paper/YSHHV3W5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.1299&json=true","fetch_graph":"https://pith.science/api/pith-number/YSHHV3W5CQWNI2WY63QFBJIPCU/graph.json","fetch_events":"https://pith.science/api/pith-number/YSHHV3W5CQWNI2WY63QFBJIPCU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YSHHV3W5CQWNI2WY63QFBJIPCU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YSHHV3W5CQWNI2WY63QFBJIPCU/action/storage_attestation","attest_author":"https://pith.science/pith/YSHHV3W5CQWNI2WY63QFBJIPCU/action/author_attestation","sign_citation":"https://pith.science/pith/YSHHV3W5CQWNI2WY63QFBJIPCU/action/citation_signature","submit_replication":"https://pith.science/pith/YSHHV3W5CQWNI2WY63QFBJIPCU/action/replication_record"}},"created_at":"2026-05-18T02:50:23.557456+00:00","updated_at":"2026-05-18T02:50:23.557456+00:00"}