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In this note we consider the maximal Beurling transform associated with squares, namely, $B^{*}_Sf(z)=\\displaystyle\\sup_{\\varepsilon >0}\\left|\\int_{w\\notin Q(0,\\varepsilon)}f(z-w) \\frac{1}{w^2} \\,dw \\right|$, $z\\in\\mathbb C$, $Q(0,\\varepsilon)$ being the squar"},"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":"1404.2196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-04-08T16:29:35Z","cross_cats_sorted":[],"title_canon_sha256":"810aca8840529e64be7372b32687395f8c75184cd724330eb03ddcd95556db49","abstract_canon_sha256":"8e859ab3046b8d1a8c6f2986e24cce3b6251cfd1c9bcdf84521ce1114eca4805"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:38.264725Z","signature_b64":"eVba+PIYIzze9Aa4HuL7I9F7QlBwKJjIzFEwArPsN9pX/gGQ8j2JbdW+r49cMaqqF/XkuicXGbhKvZQpx9qkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b924079d03b22766826aad181247f698c78e737fdc4a248705ce0551c112e4f5","last_reissued_at":"2026-05-18T02:54:38.264121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:38.264121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The maximal Beurling transform associated with squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Anna Bosch-Cam\\'os, Joan Mateu, Joan Orobitg","submitted_at":"2014-04-08T16:29:35Z","abstract_excerpt":"It is known that the improved Cotlar's inequality $B^{*}f(z) \\le C M(Bf)(z)$, $z\\in\\mathbb C$, holds for the Beurling transform $B$, the maximal Beurling transform $B^{*}f(z)=$ $\\displaystyle\\sup_{\\varepsilon >0}\\left|\\int_{|w|>\\varepsilon}f(z-w) \\frac{1}{w^2} \\,dw\\right|$, $z\\in\\mathbb C$, and the Hardy--Littlewood maximal operator $M$. In this note we consider the maximal Beurling transform associated with squares, namely, $B^{*}_Sf(z)=\\displaystyle\\sup_{\\varepsilon >0}\\left|\\int_{w\\notin Q(0,\\varepsilon)}f(z-w) \\frac{1}{w^2} \\,dw \\right|$, $z\\in\\mathbb C$, $Q(0,\\varepsilon)$ being the squar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2196","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":"1404.2196","created_at":"2026-05-18T02:54:38.264204+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.2196v1","created_at":"2026-05-18T02:54:38.264204+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2196","created_at":"2026-05-18T02:54:38.264204+00:00"},{"alias_kind":"pith_short_12","alias_value":"XESAPHIDWITW","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"XESAPHIDWITWNATK","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"XESAPHID","created_at":"2026-05-18T12:28:57.508820+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/XESAPHIDWITWNATKVUMBER7WTD","json":"https://pith.science/pith/XESAPHIDWITWNATKVUMBER7WTD.json","graph_json":"https://pith.science/api/pith-number/XESAPHIDWITWNATKVUMBER7WTD/graph.json","events_json":"https://pith.science/api/pith-number/XESAPHIDWITWNATKVUMBER7WTD/events.json","paper":"https://pith.science/paper/XESAPHID"},"agent_actions":{"view_html":"https://pith.science/pith/XESAPHIDWITWNATKVUMBER7WTD","download_json":"https://pith.science/pith/XESAPHIDWITWNATKVUMBER7WTD.json","view_paper":"https://pith.science/paper/XESAPHID","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.2196&json=true","fetch_graph":"https://pith.science/api/pith-number/XESAPHIDWITWNATKVUMBER7WTD/graph.json","fetch_events":"https://pith.science/api/pith-number/XESAPHIDWITWNATKVUMBER7WTD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XESAPHIDWITWNATKVUMBER7WTD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XESAPHIDWITWNATKVUMBER7WTD/action/storage_attestation","attest_author":"https://pith.science/pith/XESAPHIDWITWNATKVUMBER7WTD/action/author_attestation","sign_citation":"https://pith.science/pith/XESAPHIDWITWNATKVUMBER7WTD/action/citation_signature","submit_replication":"https://pith.science/pith/XESAPHIDWITWNATKVUMBER7WTD/action/replication_record"}},"created_at":"2026-05-18T02:54:38.264204+00:00","updated_at":"2026-05-18T02:54:38.264204+00:00"}