{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ME4BJBT3CPW6NOW2QYZ4WRRE2D","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":"9442fe42975c28923dd7ce863e2c86752e3abaa0c22ec985af4d821cd052fb55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-07T15:57:39Z","title_canon_sha256":"ccf80193b038eeb02fe7f666c26fca54c04f72a363fe1964254989e42e24e3bf"},"schema_version":"1.0","source":{"id":"1806.02742","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02742","created_at":"2026-05-17T23:51:14Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02742v3","created_at":"2026-05-17T23:51:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02742","created_at":"2026-05-17T23:51:14Z"},{"alias_kind":"pith_short_12","alias_value":"ME4BJBT3CPW6","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"ME4BJBT3CPW6NOW2","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"ME4BJBT3","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:9fc0b35ced79d02f0814a70f916d5453b5f5466995b7fff4af2983b2566a613e","target":"graph","created_at":"2026-05-17T23:51:14Z","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":"Utilising some recent ideas from our bilinear bi-parameter theory, we give an efficient proof of a two-weight Bloom type inequality for iterated commutators of linear bi-parameter singular integrals. We prove that if $T$ is a bi-parameter singular integral satisfying the assumptions of the bi-parameter representation theorem, then $$ \\| [b_k,\\cdots[b_2, [b_1, T]]\\cdots]\\|_{L^p(\\mu) \\to L^p(\\lambda)} \\lesssim_{[\\mu]_{A_p}, [\\lambda]_{A_p}} \\prod_{i=1}^k\\|b_i\\|_{\\operatorname{bmo}(\\nu^{\\theta_i})} , $$ where $p \\in (1,\\infty)$, $\\theta_i \\in [0,1]$, $\\sum_{i=1}^k\\theta_i=1$, $\\mu, \\lambda \\in A_","authors_text":"Emil Vuorinen, Henri Martikainen, Kangwei Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-07T15:57:39Z","title":"Bloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02742","kind":"arxiv","version":3},"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":"sha256:74c61a0928bdd3f8213ab553a4f055c7865be1c78c2f2d965a99217fd740d97e","target":"record","created_at":"2026-05-17T23:51:14Z","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":"9442fe42975c28923dd7ce863e2c86752e3abaa0c22ec985af4d821cd052fb55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-07T15:57:39Z","title_canon_sha256":"ccf80193b038eeb02fe7f666c26fca54c04f72a363fe1964254989e42e24e3bf"},"schema_version":"1.0","source":{"id":"1806.02742","kind":"arxiv","version":3}},"canonical_sha256":"613814867b13ede6bada8633cb4624d0efc961f88543a5d11eb0329bfdc40a3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"613814867b13ede6bada8633cb4624d0efc961f88543a5d11eb0329bfdc40a3e","first_computed_at":"2026-05-17T23:51:14.508828Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:14.508828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iof5/+3Ob43uodp5dZUd7V2WVrFo9gufy8YbKrXIecCtKiF3H6H0gw5o4umaxDp0txdBFDls49GFQWy7tjLFDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:14.509392Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.02742","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74c61a0928bdd3f8213ab553a4f055c7865be1c78c2f2d965a99217fd740d97e","sha256:9fc0b35ced79d02f0814a70f916d5453b5f5466995b7fff4af2983b2566a613e"],"state_sha256":"fde91c2aa1513407631f7b0fb9c9faa4d88ae4213f0c6a7a120e2ddf93783c27"}