{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:LJNXTCAW7D55IY2Q5WIWKKDXZP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"704f483913b90d61ffbadee094e08734ee7a1ad08e67ebc5bcc241be4c2925f7","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1997-11-24T00:00:00Z","title_canon_sha256":"a036d894cff2187b547009bef08eeb041d880f0b0ea3c32fe13d5c4a0e8e3721"},"schema_version":"1.0","source":{"id":"math/9711210","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9711210","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/9711210v1","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9711210","created_at":"2026-05-18T01:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"LJNXTCAW7D55","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"LJNXTCAW7D55IY2Q","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"LJNXTCAW","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:b094e1d14439c042f77ec576e6653e42625e0cb4fc2f04f80204f043891fb9be","target":"graph","created_at":"2026-05-18T01:05:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In the paper we consider Calder\\'{o}n-Zygmund operators in nonhomogeneous spaces. We are going to prove the analogs of classical results for homogeneous spaces. Namely, we prove that a Calder\\'{o}n-Zygmund operator is of weak type if it is bounded in $L^2$. We also prove several versions of Cotlar's inequality for maximal singular operator. One version of Cotlar's inequality (a simpler one) is proved in Euclidean setting, another one in a more abstract setting when Besicovich covering lemma is not available. We obtain also the weak type of maximal singular operator from these inequalities.","authors_text":"Alexander Volberg, Fedor Nazarov, Sergei Treil","cross_cats":[],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"1997-11-24T00:00:00Z","title":"Weak type estimates and Cotlar inequalities for Calder\\'{o}n-Zygmund operators in nonhomogeneous spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9711210","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:849b727b7109185332f24e493be58c932a32119b898f4bb803d240c28b51cf78","target":"record","created_at":"2026-05-18T01:05:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"704f483913b90d61ffbadee094e08734ee7a1ad08e67ebc5bcc241be4c2925f7","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1997-11-24T00:00:00Z","title_canon_sha256":"a036d894cff2187b547009bef08eeb041d880f0b0ea3c32fe13d5c4a0e8e3721"},"schema_version":"1.0","source":{"id":"math/9711210","kind":"arxiv","version":1}},"canonical_sha256":"5a5b798816f8fbd46350ed91652877cbcfdc4d7ce2412ab84629679e7d59e999","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a5b798816f8fbd46350ed91652877cbcfdc4d7ce2412ab84629679e7d59e999","first_computed_at":"2026-05-18T01:05:34.651748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:34.651748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PTK01wc8GAxDpijtlmho0SBBQxag5dE+RVOBpLZ3cZLkzV1ewdKjZiJKTG7tmso6KeFFaUXzMtr9fgmzbtBlDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:34.652478Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9711210","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:849b727b7109185332f24e493be58c932a32119b898f4bb803d240c28b51cf78","sha256:b094e1d14439c042f77ec576e6653e42625e0cb4fc2f04f80204f043891fb9be"],"state_sha256":"161e070c9c67a08422cc9f905d258a2e681c0406ff02ba0d85e75b85efc1b6fb"}