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This article is primarily concerned with the study of endpoint boundedness for classical singular integral operators in the context of the space $ \\mathrm{CMO}_{\\mathcal{L}}(\\mathbb{R}^n) $, consisting of functions of vanishing mean oscillation associated with $ \\mathcal{L} $.\n  We establish the following main results: (i) the standard Hardy--Littlewood maximal operator is bounded on $\\mathrm"},"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":"2504.16827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-04-23T15:43:52Z","cross_cats_sorted":[],"title_canon_sha256":"7abdb35638f50bab3ab317449d82c505a5b88d8adcec576bebf19623f4962b2a","abstract_canon_sha256":"6cc068707d8dfd432663fa532fddfe9468bb2049227e5e2fae61c881e53715fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:53:05.021476Z","signature_b64":"d7sJDehUaSieT+bVXd+aJkBIlfWxz+Qvh/WSVeVc7EW0dgX6HezRQqCm6m9s5641jov+GbIl80wPTzeFvNJbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61c703e1ea64f78b7fb17a99556e2b70d36b169d986d22c247e387d5712c4591","last_reissued_at":"2026-07-05T10:53:05.021059Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:53:05.021059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Endpoint boundedness of singular integrals: CMO space associated to Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ji Li, Liangchuan Wu, Xueting Han","submitted_at":"2025-04-23T15:43:52Z","abstract_excerpt":"Let $ \\mathcal{L} = -\\Delta + V $ be a Schr\\\"odinger operator acting on $ L^2(\\mathbb{R}^n) $, where the nonnegative potential $ V $ belongs to the reverse H\\\"older class $ RH_q $ for some $ q \\geq n/2 $. 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