{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UQPQTITXABB2WXL4DLTBGV5GTY","short_pith_number":"pith:UQPQTITX","schema_version":"1.0","canonical_sha256":"a41f09a2770043ab5d7c1ae61357a69e2a0d253d29585f67bf53d52c2ee79ddd","source":{"kind":"arxiv","id":"1801.09832","version":2},"attestation_state":"computed","paper":{"title":"Characterizations for inner functions in certain function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Atte Reijonen, Toshiyuki Sugawa","submitted_at":"2018-01-30T02:48:32Z","abstract_excerpt":"For $\\frac12<p<\\infty$, $0<q<\\infty$ and a certain two-sided doubling weight $\\omega$, we characterize those inner functions $\\Theta$ for which $$\\|\\Theta'\\|_{A^{p,q}_\\omega}^q=\\int_0^1 \\left(\\int_0^{2\\pi} |\\Theta'(re^{i\\theta})|^p d\\theta\\right)^{q/p}\n  \\omega(r)\\,dr<\\infty.$$ Then we show a modified version of this result for $p\\ge q$. Moreover, two additional characterizations for inner functions whose derivative belongs to the Bergman space $A_\\omega^{p,p}$ are given."},"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":"1801.09832","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-01-30T02:48:32Z","cross_cats_sorted":[],"title_canon_sha256":"0c6e59d4a1998a98c11cd0afa308497cec3ef6ded13c811f40206cb506bbcf9e","abstract_canon_sha256":"4deb3c05091dca8ae629299bd0f736a5a9cce702303b7cf5f10b19daa23a3f17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:15.157631Z","signature_b64":"oTfEkT0BbANBEL8UVQd6zd6S/q8nZtwpbJXgmm6STLuxTAj6WpSylrJkDfa7+ST50hahg8vi+arY1U30Xf5fAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a41f09a2770043ab5d7c1ae61357a69e2a0d253d29585f67bf53d52c2ee79ddd","last_reissued_at":"2026-05-18T00:01:15.157069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:15.157069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizations for inner functions in certain function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Atte Reijonen, Toshiyuki Sugawa","submitted_at":"2018-01-30T02:48:32Z","abstract_excerpt":"For $\\frac12<p<\\infty$, $0<q<\\infty$ and a certain two-sided doubling weight $\\omega$, we characterize those inner functions $\\Theta$ for which $$\\|\\Theta'\\|_{A^{p,q}_\\omega}^q=\\int_0^1 \\left(\\int_0^{2\\pi} |\\Theta'(re^{i\\theta})|^p d\\theta\\right)^{q/p}\n  \\omega(r)\\,dr<\\infty.$$ Then we show a modified version of this result for $p\\ge q$. Moreover, two additional characterizations for inner functions whose derivative belongs to the Bergman space $A_\\omega^{p,p}$ are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09832","kind":"arxiv","version":2},"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":"1801.09832","created_at":"2026-05-18T00:01:15.157148+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.09832v2","created_at":"2026-05-18T00:01:15.157148+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09832","created_at":"2026-05-18T00:01:15.157148+00:00"},{"alias_kind":"pith_short_12","alias_value":"UQPQTITXABB2","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"UQPQTITXABB2WXL4","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"UQPQTITX","created_at":"2026-05-18T12:32:56.356000+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/UQPQTITXABB2WXL4DLTBGV5GTY","json":"https://pith.science/pith/UQPQTITXABB2WXL4DLTBGV5GTY.json","graph_json":"https://pith.science/api/pith-number/UQPQTITXABB2WXL4DLTBGV5GTY/graph.json","events_json":"https://pith.science/api/pith-number/UQPQTITXABB2WXL4DLTBGV5GTY/events.json","paper":"https://pith.science/paper/UQPQTITX"},"agent_actions":{"view_html":"https://pith.science/pith/UQPQTITXABB2WXL4DLTBGV5GTY","download_json":"https://pith.science/pith/UQPQTITXABB2WXL4DLTBGV5GTY.json","view_paper":"https://pith.science/paper/UQPQTITX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.09832&json=true","fetch_graph":"https://pith.science/api/pith-number/UQPQTITXABB2WXL4DLTBGV5GTY/graph.json","fetch_events":"https://pith.science/api/pith-number/UQPQTITXABB2WXL4DLTBGV5GTY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UQPQTITXABB2WXL4DLTBGV5GTY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UQPQTITXABB2WXL4DLTBGV5GTY/action/storage_attestation","attest_author":"https://pith.science/pith/UQPQTITXABB2WXL4DLTBGV5GTY/action/author_attestation","sign_citation":"https://pith.science/pith/UQPQTITXABB2WXL4DLTBGV5GTY/action/citation_signature","submit_replication":"https://pith.science/pith/UQPQTITXABB2WXL4DLTBGV5GTY/action/replication_record"}},"created_at":"2026-05-18T00:01:15.157148+00:00","updated_at":"2026-05-18T00:01:15.157148+00:00"}