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We prove a weighted L^2 estimate of the maximal commutator operator \\sup_{R>0}|[b, S_R^\\lambda(H)](f)|, where [b, S_R^\\lambda(H)](f) = bS_R^\\lambda(H) f - S_R^\\lambda(H)(bf) is the commutator of a BMO function b and the Bochner-Riesz means S_R^\\lambda(H) for the Hermite operator H. As an application, we obtain the almost everywhere convergence of [b, S_R^\\lambda(H)](f) for large \\lambda and f\\in L^p(\\mathbb{R}^n)."},"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":"2303.05211","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2023-03-09T12:31:18Z","cross_cats_sorted":[],"title_canon_sha256":"e2a803db7c72138c9c8a44fc8700fd7e8c6cb2d93b012d204443741c7bdaac23","abstract_canon_sha256":"44f8994c7b7b72758e66a1a56dbaccd8c0542b9a8013355b41ae740b1ab14be6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:49:38.426982Z","signature_b64":"kP0HuOejr4exL7Ghr1tkdlyl3kbSm28uMT+JlXFEJIZ/fVwe57b4Pee+lVbB/iIPGmiQZUilEeZ/a7qR2xbCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39287b9fed0a6d1649580550021776e1d00575652673e6b4852c9be928b6046f","last_reissued_at":"2026-07-05T05:49:38.426557Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:49:38.426557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A weighted L^2 estimate of Commutators of Bochner-Riesz Operators for Hermite operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Peng Chen, Xixi Lin","submitted_at":"2023-03-09T12:31:18Z","abstract_excerpt":"Let H be the Hermite operator -\\Delta +|x|^2 on \\mathbb{R}^n. We prove a weighted L^2 estimate of the maximal commutator operator \\sup_{R>0}|[b, S_R^\\lambda(H)](f)|, where [b, S_R^\\lambda(H)](f) = bS_R^\\lambda(H) f - S_R^\\lambda(H)(bf) is the commutator of a BMO function b and the Bochner-Riesz means S_R^\\lambda(H) for the Hermite operator H. As an application, we obtain the almost everywhere convergence of [b, S_R^\\lambda(H)](f) for large \\lambda and f\\in L^p(\\mathbb{R}^n)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.05211","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.05211/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2303.05211","created_at":"2026-07-05T05:49:38.426613+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.05211v1","created_at":"2026-07-05T05:49:38.426613+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.05211","created_at":"2026-07-05T05:49:38.426613+00:00"},{"alias_kind":"pith_short_12","alias_value":"HEUHXH7NBJWR","created_at":"2026-07-05T05:49:38.426613+00:00"},{"alias_kind":"pith_short_16","alias_value":"HEUHXH7NBJWRMSKY","created_at":"2026-07-05T05:49:38.426613+00:00"},{"alias_kind":"pith_short_8","alias_value":"HEUHXH7N","created_at":"2026-07-05T05:49:38.426613+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.16116","citing_title":"Difference and Wavelet Characterizations of Distances from Functions in Lipschitz Spaces to Their Subspaces","ref_index":11,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HEUHXH7NBJWRMSKYAVIAEF3W4H","json":"https://pith.science/pith/HEUHXH7NBJWRMSKYAVIAEF3W4H.json","graph_json":"https://pith.science/api/pith-number/HEUHXH7NBJWRMSKYAVIAEF3W4H/graph.json","events_json":"https://pith.science/api/pith-number/HEUHXH7NBJWRMSKYAVIAEF3W4H/events.json","paper":"https://pith.science/paper/HEUHXH7N"},"agent_actions":{"view_html":"https://pith.science/pith/HEUHXH7NBJWRMSKYAVIAEF3W4H","download_json":"https://pith.science/pith/HEUHXH7NBJWRMSKYAVIAEF3W4H.json","view_paper":"https://pith.science/paper/HEUHXH7N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.05211&json=true","fetch_graph":"https://pith.science/api/pith-number/HEUHXH7NBJWRMSKYAVIAEF3W4H/graph.json","fetch_events":"https://pith.science/api/pith-number/HEUHXH7NBJWRMSKYAVIAEF3W4H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HEUHXH7NBJWRMSKYAVIAEF3W4H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HEUHXH7NBJWRMSKYAVIAEF3W4H/action/storage_attestation","attest_author":"https://pith.science/pith/HEUHXH7NBJWRMSKYAVIAEF3W4H/action/author_attestation","sign_citation":"https://pith.science/pith/HEUHXH7NBJWRMSKYAVIAEF3W4H/action/citation_signature","submit_replication":"https://pith.science/pith/HEUHXH7NBJWRMSKYAVIAEF3W4H/action/replication_record"}},"created_at":"2026-07-05T05:49:38.426613+00:00","updated_at":"2026-07-05T05:49:38.426613+00:00"}