{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6JICMZAKZOVOSUBV47PFJORNDY","short_pith_number":"pith:6JICMZAK","schema_version":"1.0","canonical_sha256":"f25026640acbaae95035e7de54ba2d1e357507daa60e0348b9ce159ad7dc085e","source":{"kind":"arxiv","id":"1501.03744","version":1},"attestation_state":"computed","paper":{"title":"On a Weighted Singular Integral Operator with Shifts and Slowly Oscillating Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexei Yu. Karlovich, Amarino B. Lebre, Yuri I. Karlovich","submitted_at":"2015-01-15T17:14:58Z","abstract_excerpt":"Let $\\alpha,\\beta$ be orientation-preserving diffeomorphism (shifts) of $\\mathbb{R}_+=(0,\\infty)$ onto itself with the only fixed points $0$ and $\\infty$ and $U_\\alpha,U_\\beta$ be the isometric shift operators on $L^p(\\mathbb{R}_+)$ given by $U_\\alpha f=(\\alpha')^{1/p}(f\\circ\\alpha)$, $U_\\beta f=(\\beta')^{1/p}(f\\circ\\beta)$, and $P_2^\\pm=(I\\pm S_2)/2$ where \\[ (S_2 f)(t):=\\frac{1}{\\pi i}\\int\\limits_0^\\infty \\left(\\frac{t}{\\tau}\\right)^{1/2-1/p}\\frac{f(\\tau)}{\\tau-t}\\,d\\tau, \\quad t\\in\\mathbb{R}_+, \\] is the weighted Cauchy singular integral operator. We prove that if $\\alpha',\\beta'$ and $c,d$"},"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":"1501.03744","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-01-15T17:14:58Z","cross_cats_sorted":[],"title_canon_sha256":"bf66706ed023f79990ace96a7d994b67a7e373bc35516327109a263eb330ecda","abstract_canon_sha256":"046a86afe66861ef731aa795005a19e0a1685b7571f8fd0c4f38b9151227e177"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:17.906526Z","signature_b64":"ympzWKfXwW4IDtgiTEMJbqxpwu6gxa4tGunwIXRAaFRPsTGOmpIL0tN4DGftrB7alGjFUTKXTQ4TDtddbEM/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f25026640acbaae95035e7de54ba2d1e357507daa60e0348b9ce159ad7dc085e","last_reissued_at":"2026-05-18T02:29:17.906130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:17.906130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a Weighted Singular Integral Operator with Shifts and Slowly Oscillating Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexei Yu. Karlovich, Amarino B. Lebre, Yuri I. Karlovich","submitted_at":"2015-01-15T17:14:58Z","abstract_excerpt":"Let $\\alpha,\\beta$ be orientation-preserving diffeomorphism (shifts) of $\\mathbb{R}_+=(0,\\infty)$ onto itself with the only fixed points $0$ and $\\infty$ and $U_\\alpha,U_\\beta$ be the isometric shift operators on $L^p(\\mathbb{R}_+)$ given by $U_\\alpha f=(\\alpha')^{1/p}(f\\circ\\alpha)$, $U_\\beta f=(\\beta')^{1/p}(f\\circ\\beta)$, and $P_2^\\pm=(I\\pm S_2)/2$ where \\[ (S_2 f)(t):=\\frac{1}{\\pi i}\\int\\limits_0^\\infty \\left(\\frac{t}{\\tau}\\right)^{1/2-1/p}\\frac{f(\\tau)}{\\tau-t}\\,d\\tau, \\quad t\\in\\mathbb{R}_+, \\] is the weighted Cauchy singular integral operator. We prove that if $\\alpha',\\beta'$ and $c,d$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03744","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":"1501.03744","created_at":"2026-05-18T02:29:17.906193+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.03744v1","created_at":"2026-05-18T02:29:17.906193+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03744","created_at":"2026-05-18T02:29:17.906193+00:00"},{"alias_kind":"pith_short_12","alias_value":"6JICMZAKZOVO","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6JICMZAKZOVOSUBV","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6JICMZAK","created_at":"2026-05-18T12:29:07.941421+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/6JICMZAKZOVOSUBV47PFJORNDY","json":"https://pith.science/pith/6JICMZAKZOVOSUBV47PFJORNDY.json","graph_json":"https://pith.science/api/pith-number/6JICMZAKZOVOSUBV47PFJORNDY/graph.json","events_json":"https://pith.science/api/pith-number/6JICMZAKZOVOSUBV47PFJORNDY/events.json","paper":"https://pith.science/paper/6JICMZAK"},"agent_actions":{"view_html":"https://pith.science/pith/6JICMZAKZOVOSUBV47PFJORNDY","download_json":"https://pith.science/pith/6JICMZAKZOVOSUBV47PFJORNDY.json","view_paper":"https://pith.science/paper/6JICMZAK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.03744&json=true","fetch_graph":"https://pith.science/api/pith-number/6JICMZAKZOVOSUBV47PFJORNDY/graph.json","fetch_events":"https://pith.science/api/pith-number/6JICMZAKZOVOSUBV47PFJORNDY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6JICMZAKZOVOSUBV47PFJORNDY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6JICMZAKZOVOSUBV47PFJORNDY/action/storage_attestation","attest_author":"https://pith.science/pith/6JICMZAKZOVOSUBV47PFJORNDY/action/author_attestation","sign_citation":"https://pith.science/pith/6JICMZAKZOVOSUBV47PFJORNDY/action/citation_signature","submit_replication":"https://pith.science/pith/6JICMZAKZOVOSUBV47PFJORNDY/action/replication_record"}},"created_at":"2026-05-18T02:29:17.906193+00:00","updated_at":"2026-05-18T02:29:17.906193+00:00"}