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Finally, we will use some of the ideas from these proofs to (among other things) obtain quantitative weighted norm inequalities for these operators and also use them to pro"},"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":"1507.04032","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-14T21:29:00Z","cross_cats_sorted":[],"title_canon_sha256":"8c98909434d23c36ea9e7356cb58fb8e286691a732555ac28f436ba58d16949a","abstract_canon_sha256":"e88fe098904e1bb6e897146c1b3058be4b448a49dda88da5307d66301ba89007"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:33.851895Z","signature_b64":"Y98C5KyRWVcOoCR3dq+a4rYYmJc4CA2HLENfIE3xvPeCnbPDnJEkJeMwCfVSGLpDnQbZ8XG5dtW3Bwb4KZczCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d1003129ed6bb65930f1cd42ef6f5101a61c1f5ee6fc70bed391e6a8f1b3051","last_reissued_at":"2026-05-18T00:40:33.851220Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:33.851220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matrix weighted norm inequalities for commutators and paraproducts with matrix symbols","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Hyun-Kyoung Kwon, Joshua Isralowitz, Sandra Pott","submitted_at":"2015-07-14T21:29:00Z","abstract_excerpt":"Let $B$ be a locally integrable matrix function, $W$ a matrix A${}_p$ weight with $1 < p < \\infty$, and $T$ be any of the Riesz transforms. 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