{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1996:ZXXIS2VJJD4UJMQECTGXAPVJTE","short_pith_number":"pith:ZXXIS2VJ","schema_version":"1.0","canonical_sha256":"cdee896aa948f944b20414cd703ea99915ae3928bdda46c1e00223690ece4a21","source":{"kind":"arxiv","id":"math/9601220","version":1},"attestation_state":"computed","paper":{"title":"Spherical maximal operators on radial functions","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andreas Seeger, James Wright, Stephen Wainger","submitted_at":"1996-01-01T00:00:00Z","abstract_excerpt":"Let $A_tf(x)=\\int f(x+ty)d\\sigma(y)$ denote the spherical means in $\\Bbb R^d$ ($d\\sigma$ is surface measure on $S^{d-1}$, normalized to $1$). We prove sharp estimates for the maximal function $M_E f(x)=\\sup_{t\\in E}|A_tf(x)|$ where $E$ is a fixed set in $\\Bbb R^+$ and $f$ is a {\\it radial} function $\\in L^p(\\Bbb R^d)$. Let $p_d=d/(d-1)$ (the critical exponent of Stein's maximal function). For the cases (i) $p<p_d$, $d\\ge 2$ and (ii) $p=p_d$, $d\\ge 3$, and for $p\\le q\\le\\infty$ we prove necessary and sufficient conditions for $L^p\\to L^{p,q}$ boundedness of the operator $M_E$."},"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":"math/9601220","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1996-01-01T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"bd5b1453242bbf7a50a6b12af4dcb52a6700c542e252087b9f8940757d148160","abstract_canon_sha256":"d0f9cf8d3ad6eb587093ec22364d9d96d7c6658c48be3821cd3cd027ab240c48"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:47.836679Z","signature_b64":"n1wqhirX7RIwGWRKFgAJ9/iUIQhVyPSh6Lrq9JwVxOWpMaBD0P1XLnXL5+1NK9iBlZitzLwbppgAqC/Nx3cQBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdee896aa948f944b20414cd703ea99915ae3928bdda46c1e00223690ece4a21","last_reissued_at":"2026-05-18T01:05:47.836194Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:47.836194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spherical maximal operators on radial functions","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andreas Seeger, James Wright, Stephen Wainger","submitted_at":"1996-01-01T00:00:00Z","abstract_excerpt":"Let $A_tf(x)=\\int f(x+ty)d\\sigma(y)$ denote the spherical means in $\\Bbb R^d$ ($d\\sigma$ is surface measure on $S^{d-1}$, normalized to $1$). We prove sharp estimates for the maximal function $M_E f(x)=\\sup_{t\\in E}|A_tf(x)|$ where $E$ is a fixed set in $\\Bbb R^+$ and $f$ is a {\\it radial} function $\\in L^p(\\Bbb R^d)$. Let $p_d=d/(d-1)$ (the critical exponent of Stein's maximal function). For the cases (i) $p<p_d$, $d\\ge 2$ and (ii) $p=p_d$, $d\\ge 3$, and for $p\\le q\\le\\infty$ we prove necessary and sufficient conditions for $L^p\\to L^{p,q}$ boundedness of the operator $M_E$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9601220","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":"math/9601220","created_at":"2026-05-18T01:05:47.836273+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9601220v1","created_at":"2026-05-18T01:05:47.836273+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9601220","created_at":"2026-05-18T01:05:47.836273+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZXXIS2VJJD4U","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZXXIS2VJJD4UJMQE","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZXXIS2VJ","created_at":"2026-05-18T12:25:48.327863+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/ZXXIS2VJJD4UJMQECTGXAPVJTE","json":"https://pith.science/pith/ZXXIS2VJJD4UJMQECTGXAPVJTE.json","graph_json":"https://pith.science/api/pith-number/ZXXIS2VJJD4UJMQECTGXAPVJTE/graph.json","events_json":"https://pith.science/api/pith-number/ZXXIS2VJJD4UJMQECTGXAPVJTE/events.json","paper":"https://pith.science/paper/ZXXIS2VJ"},"agent_actions":{"view_html":"https://pith.science/pith/ZXXIS2VJJD4UJMQECTGXAPVJTE","download_json":"https://pith.science/pith/ZXXIS2VJJD4UJMQECTGXAPVJTE.json","view_paper":"https://pith.science/paper/ZXXIS2VJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9601220&json=true","fetch_graph":"https://pith.science/api/pith-number/ZXXIS2VJJD4UJMQECTGXAPVJTE/graph.json","fetch_events":"https://pith.science/api/pith-number/ZXXIS2VJJD4UJMQECTGXAPVJTE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZXXIS2VJJD4UJMQECTGXAPVJTE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZXXIS2VJJD4UJMQECTGXAPVJTE/action/storage_attestation","attest_author":"https://pith.science/pith/ZXXIS2VJJD4UJMQECTGXAPVJTE/action/author_attestation","sign_citation":"https://pith.science/pith/ZXXIS2VJJD4UJMQECTGXAPVJTE/action/citation_signature","submit_replication":"https://pith.science/pith/ZXXIS2VJJD4UJMQECTGXAPVJTE/action/replication_record"}},"created_at":"2026-05-18T01:05:47.836273+00:00","updated_at":"2026-05-18T01:05:47.836273+00:00"}