{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BEL6KWIBRTDOOTO7SDJCAOLRVJ","short_pith_number":"pith:BEL6KWIB","schema_version":"1.0","canonical_sha256":"0917e559018cc6e74ddf90d2203971aa6480751f97123fbdae0f9f4b63339d23","source":{"kind":"arxiv","id":"1204.2135","version":2},"attestation_state":"computed","paper":{"title":"The fractional Riesz transform and an exponential potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MG"],"primary_cat":"math.AP","authors_text":"Alexander Volberg, Benjamin Jaye, Fedor Nazarov","submitted_at":"2012-04-10T13:09:19Z","abstract_excerpt":"In this paper we study the $s$-dimensional Riesz transform of a finite measure $\\mu$ in $\\mathbf{R}^d$, with $s\\in (d-1,d)$. We show that the boundedness of the Riesz transform of $\\mu$ implies that a nonlinear potential of exponential type is finite $\\mu$-almost everywhere. It appears to be the first result of this type for $s>1$."},"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":"1204.2135","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-10T13:09:19Z","cross_cats_sorted":["math.CA","math.MG"],"title_canon_sha256":"e1027ab5851727c940979c8cd21514d0a6665b2f2616b320b15190db177bea6a","abstract_canon_sha256":"19997a987bb5fd9f5492b9920219d34a35fdcec487846ba1921c67c956fe62b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:42.179712Z","signature_b64":"6uTuucBeb8W3hqkdOlcWYTy8ClpJY27H79hN+cubbyb903KqoJO7t9DSaHpZcz+8EFECHm7Aef2Qaa1WdngKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0917e559018cc6e74ddf90d2203971aa6480751f97123fbdae0f9f4b63339d23","last_reissued_at":"2026-05-18T03:43:42.179069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:42.179069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The fractional Riesz transform and an exponential potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MG"],"primary_cat":"math.AP","authors_text":"Alexander Volberg, Benjamin Jaye, Fedor Nazarov","submitted_at":"2012-04-10T13:09:19Z","abstract_excerpt":"In this paper we study the $s$-dimensional Riesz transform of a finite measure $\\mu$ in $\\mathbf{R}^d$, with $s\\in (d-1,d)$. We show that the boundedness of the Riesz transform of $\\mu$ implies that a nonlinear potential of exponential type is finite $\\mu$-almost everywhere. It appears to be the first result of this type for $s>1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2135","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":"1204.2135","created_at":"2026-05-18T03:43:42.179164+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.2135v2","created_at":"2026-05-18T03:43:42.179164+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2135","created_at":"2026-05-18T03:43:42.179164+00:00"},{"alias_kind":"pith_short_12","alias_value":"BEL6KWIBRTDO","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"BEL6KWIBRTDOOTO7","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"BEL6KWIB","created_at":"2026-05-18T12:26:58.693483+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/BEL6KWIBRTDOOTO7SDJCAOLRVJ","json":"https://pith.science/pith/BEL6KWIBRTDOOTO7SDJCAOLRVJ.json","graph_json":"https://pith.science/api/pith-number/BEL6KWIBRTDOOTO7SDJCAOLRVJ/graph.json","events_json":"https://pith.science/api/pith-number/BEL6KWIBRTDOOTO7SDJCAOLRVJ/events.json","paper":"https://pith.science/paper/BEL6KWIB"},"agent_actions":{"view_html":"https://pith.science/pith/BEL6KWIBRTDOOTO7SDJCAOLRVJ","download_json":"https://pith.science/pith/BEL6KWIBRTDOOTO7SDJCAOLRVJ.json","view_paper":"https://pith.science/paper/BEL6KWIB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.2135&json=true","fetch_graph":"https://pith.science/api/pith-number/BEL6KWIBRTDOOTO7SDJCAOLRVJ/graph.json","fetch_events":"https://pith.science/api/pith-number/BEL6KWIBRTDOOTO7SDJCAOLRVJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BEL6KWIBRTDOOTO7SDJCAOLRVJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BEL6KWIBRTDOOTO7SDJCAOLRVJ/action/storage_attestation","attest_author":"https://pith.science/pith/BEL6KWIBRTDOOTO7SDJCAOLRVJ/action/author_attestation","sign_citation":"https://pith.science/pith/BEL6KWIBRTDOOTO7SDJCAOLRVJ/action/citation_signature","submit_replication":"https://pith.science/pith/BEL6KWIBRTDOOTO7SDJCAOLRVJ/action/replication_record"}},"created_at":"2026-05-18T03:43:42.179164+00:00","updated_at":"2026-05-18T03:43:42.179164+00:00"}