{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:74TNAOE65S5WCTMF2A5YMHQY7I","short_pith_number":"pith:74TNAOE6","schema_version":"1.0","canonical_sha256":"ff26d0389eecbb614d85d03b861e18fa20a38cb369dc7a264a3efb4e74ba25ae","source":{"kind":"arxiv","id":"1204.1666","version":2},"attestation_state":"computed","paper":{"title":"Exponential decay estimates for Singular Integral operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Carlos P\\'erez, Carmen Ortiz-Caraballo, Ezequiel Rela","submitted_at":"2012-04-07T18:16:36Z","abstract_excerpt":"The following subexponential estimate for commutators is proved |[|\\{x\\in Q: |[b,T]f(x)|>tM^2f(x)\\}|\\leq c\\,e^{-\\sqrt{\\alpha\\, t\\|b\\|_{BMO}}}\\, |Q|, \\qquad t>0.\\] where $c$ and $\\alpha$ are absolute constants, $T$ is a Calder\\'on--Zygmund operator, $M$ is the Hardy Littlewood maximal function and $f$ is any function supported on the cube $Q$. It is also obtained \\[|\\{x\\in Q: |f(x)-m_f(Q)|>tM_{1/4;Q}^#(f)(x) \\}|\\le c\\, e^{-\\alpha\\,t}|Q|,\\qquad t>0,\\] where $m_f(Q)$ is the median value of $f$ on the cube $Q$ and $M_{1/4;Q}^#$ is Str\\\"omberg's local sharp maximal function. As a consequence it is "},"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":"1204.1666","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-07T18:16:36Z","cross_cats_sorted":[],"title_canon_sha256":"5bfde95834a7f84de76fb8720b6a2de3603b9c575151a822f94787b903e9d8fc","abstract_canon_sha256":"3524618ee1615aa5d50eee5e3247f177d5539f5d42b10437740182e15c9fd7b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:06.211637Z","signature_b64":"EAjjfDIDeua1brsPf93HuvRB37P7eq4ykn8cFmFAW/p7hxCyXxR7n3lpBgmDohxbKBNZCTmPjsEL26IC0syBDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff26d0389eecbb614d85d03b861e18fa20a38cb369dc7a264a3efb4e74ba25ae","last_reissued_at":"2026-05-18T03:28:06.210896Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:06.210896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponential decay estimates for Singular Integral operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Carlos P\\'erez, Carmen Ortiz-Caraballo, Ezequiel Rela","submitted_at":"2012-04-07T18:16:36Z","abstract_excerpt":"The following subexponential estimate for commutators is proved |[|\\{x\\in Q: |[b,T]f(x)|>tM^2f(x)\\}|\\leq c\\,e^{-\\sqrt{\\alpha\\, t\\|b\\|_{BMO}}}\\, |Q|, \\qquad t>0.\\] where $c$ and $\\alpha$ are absolute constants, $T$ is a Calder\\'on--Zygmund operator, $M$ is the Hardy Littlewood maximal function and $f$ is any function supported on the cube $Q$. It is also obtained \\[|\\{x\\in Q: |f(x)-m_f(Q)|>tM_{1/4;Q}^#(f)(x) \\}|\\le c\\, e^{-\\alpha\\,t}|Q|,\\qquad t>0,\\] where $m_f(Q)$ is the median value of $f$ on the cube $Q$ and $M_{1/4;Q}^#$ is Str\\\"omberg's local sharp maximal function. 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