{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:RRE3IJ5UMENAMJK4FOH335VMKX","short_pith_number":"pith:RRE3IJ5U","schema_version":"1.0","canonical_sha256":"8c49b427b4611a06255c2b8fbdf6ac55d5ccb8345d903d83d45a82e15eed49fe","source":{"kind":"arxiv","id":"1504.03091","version":1},"attestation_state":"computed","paper":{"title":"Embedding Bergman spaces into tent spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Jos\\'e \\'Angel Pel\\'aez, Jouni R\\\"atty\\\"a, Kian Sierra","submitted_at":"2015-04-13T08:08:47Z","abstract_excerpt":"Let $A^p_\\omega$ denote the Bergman space in the unit disc $\\mathbb{D}$ of the complex plane induced by a radial weight $\\omega$ with the doubling property $\\int_{r}^1\\omega(s)\\,ds\\le C\\int_{\\frac{1+r}{2}}^1\\omega(s)\\,ds$. The tent space $T^q_s(\\nu,\\omega)$ consists of functions such that\n  \\begin{equation*}\n  \\begin{split}\n  \\|f\\|_{T^q_s(\\nu,\\omega)}^q\n  =\\int_{\\mathbb{D}}\\left(\\int_{\\Gamma(\\zeta)}|f(z)|^s\\,d\\nu(z)\\right)^\\frac{q}s\\omega(\\zeta)\\,dA(\\zeta)\n  <\\infty,\\quad 0<q,s<\\infty.\n  \\end{split}\n  \\end{equation*} Here $\\Gamma(\\zeta)$ is a non-tangential approach region with vertex $\\zeta$ "},"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":"1504.03091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-04-13T08:08:47Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"019f278ad39476ef20c8a0fbef67e4a6d3a15210992e48f074432618d4d39d78","abstract_canon_sha256":"9076e1c7ff6ff858b5b6afa2a0e3ef76e1cdcb821ed3e24a4402e76c19323085"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:59.246650Z","signature_b64":"OaK3bW86aGHCAzGiMFCgRkS31olcztsCU/Nba4K+Gh5OnNS0Cbn+fNpoyt1F7kc9hRVEnxY15N8NEyfPpm9IBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c49b427b4611a06255c2b8fbdf6ac55d5ccb8345d903d83d45a82e15eed49fe","last_reissued_at":"2026-05-18T02:18:59.245949Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:59.245949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Embedding Bergman spaces into tent spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Jos\\'e \\'Angel Pel\\'aez, Jouni R\\\"atty\\\"a, Kian Sierra","submitted_at":"2015-04-13T08:08:47Z","abstract_excerpt":"Let $A^p_\\omega$ denote the Bergman space in the unit disc $\\mathbb{D}$ of the complex plane induced by a radial weight $\\omega$ with the doubling property $\\int_{r}^1\\omega(s)\\,ds\\le C\\int_{\\frac{1+r}{2}}^1\\omega(s)\\,ds$. The tent space $T^q_s(\\nu,\\omega)$ consists of functions such that\n  \\begin{equation*}\n  \\begin{split}\n  \\|f\\|_{T^q_s(\\nu,\\omega)}^q\n  =\\int_{\\mathbb{D}}\\left(\\int_{\\Gamma(\\zeta)}|f(z)|^s\\,d\\nu(z)\\right)^\\frac{q}s\\omega(\\zeta)\\,dA(\\zeta)\n  <\\infty,\\quad 0<q,s<\\infty.\n  \\end{split}\n  \\end{equation*} Here $\\Gamma(\\zeta)$ is a non-tangential approach region with vertex $\\zeta$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03091","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":"1504.03091","created_at":"2026-05-18T02:18:59.246050+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.03091v1","created_at":"2026-05-18T02:18:59.246050+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03091","created_at":"2026-05-18T02:18:59.246050+00:00"},{"alias_kind":"pith_short_12","alias_value":"RRE3IJ5UMENA","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RRE3IJ5UMENAMJK4","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RRE3IJ5U","created_at":"2026-05-18T12:29:39.896362+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/RRE3IJ5UMENAMJK4FOH335VMKX","json":"https://pith.science/pith/RRE3IJ5UMENAMJK4FOH335VMKX.json","graph_json":"https://pith.science/api/pith-number/RRE3IJ5UMENAMJK4FOH335VMKX/graph.json","events_json":"https://pith.science/api/pith-number/RRE3IJ5UMENAMJK4FOH335VMKX/events.json","paper":"https://pith.science/paper/RRE3IJ5U"},"agent_actions":{"view_html":"https://pith.science/pith/RRE3IJ5UMENAMJK4FOH335VMKX","download_json":"https://pith.science/pith/RRE3IJ5UMENAMJK4FOH335VMKX.json","view_paper":"https://pith.science/paper/RRE3IJ5U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.03091&json=true","fetch_graph":"https://pith.science/api/pith-number/RRE3IJ5UMENAMJK4FOH335VMKX/graph.json","fetch_events":"https://pith.science/api/pith-number/RRE3IJ5UMENAMJK4FOH335VMKX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RRE3IJ5UMENAMJK4FOH335VMKX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RRE3IJ5UMENAMJK4FOH335VMKX/action/storage_attestation","attest_author":"https://pith.science/pith/RRE3IJ5UMENAMJK4FOH335VMKX/action/author_attestation","sign_citation":"https://pith.science/pith/RRE3IJ5UMENAMJK4FOH335VMKX/action/citation_signature","submit_replication":"https://pith.science/pith/RRE3IJ5UMENAMJK4FOH335VMKX/action/replication_record"}},"created_at":"2026-05-18T02:18:59.246050+00:00","updated_at":"2026-05-18T02:18:59.246050+00:00"}