{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LMGMAOV73RXG3E44YB2QQT7GC7","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":"a4ce7f33fb3fa9da9628287e0db7a4e51767962c624ecccc665706c11d27255d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-08-19T13:50:51Z","title_canon_sha256":"589e6d8a6b1c60ba66f7652489477406eea30625484864d4d2951dace5f78f78"},"schema_version":"1.0","source":{"id":"1408.4339","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4339","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4339v2","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4339","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"pith_short_12","alias_value":"LMGMAOV73RXG","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LMGMAOV73RXG3E44","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LMGMAOV7","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:434d26d3ff09d4a5c9da8a3170d2bacc12b2ee21a5e7b7c2e91f750c951fc469","target":"graph","created_at":"2026-05-18T01:35:57Z","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":"We improve on several mixed weak type inequalities both for the Hardy-Littlewood maximal function and for Calder\\'on-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by Sawyer estimating the $L^{1, \\infty}(uv)$ norm of $v^{-1}T(fv)$ for special cases. The emphasis is made in proving new and more precise quantitative estimates involving the $A_p$ or $A_\\infty$ constants of the weights involved.","authors_text":"Carlos Perez, Jorgelina Recchi, Sheldy Ombrosi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-08-19T13:50:51Z","title":"Quantitative weighted mixed weak-type inequalities for classical operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4339","kind":"arxiv","version":2},"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":"sha256:5c02b48d370095106cc86c4fb53e6d1f430f73853ed1d96775782222ab6c26ab","target":"record","created_at":"2026-05-18T01:35:57Z","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":"a4ce7f33fb3fa9da9628287e0db7a4e51767962c624ecccc665706c11d27255d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-08-19T13:50:51Z","title_canon_sha256":"589e6d8a6b1c60ba66f7652489477406eea30625484864d4d2951dace5f78f78"},"schema_version":"1.0","source":{"id":"1408.4339","kind":"arxiv","version":2}},"canonical_sha256":"5b0cc03abfdc6e6d939cc075084fe617cdb364ae04154b6b0f25671756641e74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b0cc03abfdc6e6d939cc075084fe617cdb364ae04154b6b0f25671756641e74","first_computed_at":"2026-05-18T01:35:57.273276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:57.273276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TFd+tsjNdmfrPOsuPDI60q6kahfhwtxD7Kqp2ksJM4OwtIg7gp0NP1IdyAa2bYCpzcGqTsJdMEGucu7Se2mDAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:57.273842Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4339","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c02b48d370095106cc86c4fb53e6d1f430f73853ed1d96775782222ab6c26ab","sha256:434d26d3ff09d4a5c9da8a3170d2bacc12b2ee21a5e7b7c2e91f750c951fc469"],"state_sha256":"b633c60b90ee5e3fb8e6491122fb16245c14702c3e2ee67951aee750d1e9435f"}