{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LINEDEQIV5BMXQ3K23I6VOIFGI","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":"855ddf33a0753727839ddd0ff53a340a72c86f77b7e0fbd4868c446ccc30a2f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-08-15T22:33:03Z","title_canon_sha256":"c7821cd1c1b93e47ba39a819bf4dec3a7607d3d199b0d8b4ab37be1eca9c8cac"},"schema_version":"1.0","source":{"id":"1108.3109","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3109","created_at":"2026-05-18T03:19:46Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3109v4","created_at":"2026-05-18T03:19:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3109","created_at":"2026-05-18T03:19:46Z"},{"alias_kind":"pith_short_12","alias_value":"LINEDEQIV5BM","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LINEDEQIV5BMXQ3K","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LINEDEQI","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:ee75db500957cfb6c70b74fc04cf3521d5b6c2dab2459cb8176d5496feffa50c","target":"graph","created_at":"2026-05-18T03:19:46Z","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 extend the definitions of dyadic paraproduct and t-Haar multipliers to dyadic operators that depend on the complexity (m,n), for m and n positive integers. We will use the ideas developed by Nazarov and Volberg to prove that the weighted L^2(w)-norm of a paraproduct with complexity (m,n) associated to a function b\\in BMO, depends linearly on the A_2-characteristic of the weight w, linearly on the BMO-norm of b, and polynomially in the complexity. This argument provides a new proof of the linear bound for the dyadic paraproduct (the one with complexity (0,0)). Also we prove that the L^2-norm","authors_text":"Jean Carlo Moraes, Mar\\'ia Cristina Pereyra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-08-15T22:33:03Z","title":"Weighted estimates for dyadic paraproducts and t-Haar multipiers with complexity (m,n)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3109","kind":"arxiv","version":4},"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":"sha256:852997d5dda01931ec8afe3498f4afd347f518a28658577443519ab9f20b5965","target":"record","created_at":"2026-05-18T03:19:46Z","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":"855ddf33a0753727839ddd0ff53a340a72c86f77b7e0fbd4868c446ccc30a2f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-08-15T22:33:03Z","title_canon_sha256":"c7821cd1c1b93e47ba39a819bf4dec3a7607d3d199b0d8b4ab37be1eca9c8cac"},"schema_version":"1.0","source":{"id":"1108.3109","kind":"arxiv","version":4}},"canonical_sha256":"5a1a419208af42cbc36ad6d1eab905320e714b70031617c90754c224e8eee27d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a1a419208af42cbc36ad6d1eab905320e714b70031617c90754c224e8eee27d","first_computed_at":"2026-05-18T03:19:46.321368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:46.321368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FTqAHiCsgV1ndrbahm6TZEIxuvje9KVrUxDjjLxB4VtFlactCmRMlZVoqSIvKQ3hDGhd2z0D5DDIMJU7parDDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:46.322152Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3109","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:852997d5dda01931ec8afe3498f4afd347f518a28658577443519ab9f20b5965","sha256:ee75db500957cfb6c70b74fc04cf3521d5b6c2dab2459cb8176d5496feffa50c"],"state_sha256":"92a77e6500575c6e1452f3bb32b843170c3d14ae362ae9874d08a5891a74e168"}