{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UALJUUK42ETF2AATPDNSY5Q6VH","short_pith_number":"pith:UALJUUK4","schema_version":"1.0","canonical_sha256":"a0169a515cd1265d001378db2c761ea9d419125c45504869c60564e07932fff7","source":{"kind":"arxiv","id":"1906.03797","version":2},"attestation_state":"computed","paper":{"title":"Annulus Maximal Averages on Variable Hyperplanes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Joonil Kim","submitted_at":"2019-06-10T05:10:43Z","abstract_excerpt":"By giving a thin width of $0<\\delta\\ll 1$ to both a unit circle and a unit line, we set an annulus and a tube on the Euclidean plane $\\mathbb{R}^2$. Consider the maximal means $M_\\delta$ over dilations of the annulus, and $N_\\delta$ over rotations of the tube. It is known that their operator norms on $L^2(\\mathbb{R}^2)$ are $O(|\\log 1/\\delta|^{1/2})$. In this paper, we study the maximal averages $\\mathcal{M}^A_\\delta$ and $\\mathcal{N}^A_\\delta$ over those annuli and tubes now imbedded on the variable hyperplanes $(x,x_3)+\\left\\{\\left(y, \\langle A(x), y\\rangle\\right): y\\in\\mathbb{R}^2\\right\\}\\s"},"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":"1906.03797","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-06-10T05:10:43Z","cross_cats_sorted":[],"title_canon_sha256":"b65b839fb930e08b40a3f75f1f49ba0adc87b98d12fdb96fbdca0dbb6a0734af","abstract_canon_sha256":"f945b97f05f29c6a9432ac9d77c16dffeb4d6b69ed5addb4aeea7c0bd26e59b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:33:16.787863Z","signature_b64":"xcT/6o7pUADpwqctA7QNupkTTcLUfytyDPVnnchIIif/UF+ALC+tgba57qqx5x9xOsGh33GEfSisww13sJkbCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0169a515cd1265d001378db2c761ea9d419125c45504869c60564e07932fff7","last_reissued_at":"2026-07-05T01:33:16.787438Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:33:16.787438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Annulus Maximal Averages on Variable Hyperplanes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Joonil Kim","submitted_at":"2019-06-10T05:10:43Z","abstract_excerpt":"By giving a thin width of $0<\\delta\\ll 1$ to both a unit circle and a unit line, we set an annulus and a tube on the Euclidean plane $\\mathbb{R}^2$. Consider the maximal means $M_\\delta$ over dilations of the annulus, and $N_\\delta$ over rotations of the tube. It is known that their operator norms on $L^2(\\mathbb{R}^2)$ are $O(|\\log 1/\\delta|^{1/2})$. In this paper, we study the maximal averages $\\mathcal{M}^A_\\delta$ and $\\mathcal{N}^A_\\delta$ over those annuli and tubes now imbedded on the variable hyperplanes $(x,x_3)+\\left\\{\\left(y, \\langle A(x), y\\rangle\\right): y\\in\\mathbb{R}^2\\right\\}\\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03797","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1906.03797/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":"1906.03797","created_at":"2026-07-05T01:33:16.787498+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.03797v2","created_at":"2026-07-05T01:33:16.787498+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.03797","created_at":"2026-07-05T01:33:16.787498+00:00"},{"alias_kind":"pith_short_12","alias_value":"UALJUUK42ETF","created_at":"2026-07-05T01:33:16.787498+00:00"},{"alias_kind":"pith_short_16","alias_value":"UALJUUK42ETF2AAT","created_at":"2026-07-05T01:33:16.787498+00:00"},{"alias_kind":"pith_short_8","alias_value":"UALJUUK4","created_at":"2026-07-05T01:33:16.787498+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2510.14180","citing_title":"Failure of stability of a maximal operator bound for perturbed Nevo-Thangavelu means","ref_index":4,"is_internal_anchor":false},{"citing_arxiv_id":"2511.11283","citing_title":"Problems on spherical maximal functions","ref_index":51,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UALJUUK42ETF2AATPDNSY5Q6VH","json":"https://pith.science/pith/UALJUUK42ETF2AATPDNSY5Q6VH.json","graph_json":"https://pith.science/api/pith-number/UALJUUK42ETF2AATPDNSY5Q6VH/graph.json","events_json":"https://pith.science/api/pith-number/UALJUUK42ETF2AATPDNSY5Q6VH/events.json","paper":"https://pith.science/paper/UALJUUK4"},"agent_actions":{"view_html":"https://pith.science/pith/UALJUUK42ETF2AATPDNSY5Q6VH","download_json":"https://pith.science/pith/UALJUUK42ETF2AATPDNSY5Q6VH.json","view_paper":"https://pith.science/paper/UALJUUK4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.03797&json=true","fetch_graph":"https://pith.science/api/pith-number/UALJUUK42ETF2AATPDNSY5Q6VH/graph.json","fetch_events":"https://pith.science/api/pith-number/UALJUUK42ETF2AATPDNSY5Q6VH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UALJUUK42ETF2AATPDNSY5Q6VH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UALJUUK42ETF2AATPDNSY5Q6VH/action/storage_attestation","attest_author":"https://pith.science/pith/UALJUUK42ETF2AATPDNSY5Q6VH/action/author_attestation","sign_citation":"https://pith.science/pith/UALJUUK42ETF2AATPDNSY5Q6VH/action/citation_signature","submit_replication":"https://pith.science/pith/UALJUUK42ETF2AATPDNSY5Q6VH/action/replication_record"}},"created_at":"2026-07-05T01:33:16.787498+00:00","updated_at":"2026-07-05T01:33:16.787498+00:00"}