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In this article, by using the reducing operators of $W$, we introduce matrix-weighted Campanato spaces $\\mathcal L_{p,q,s,W}$. When $p\\in(0,1]$, applying the atomic and the finite atomic characterizations of the matrix-weighted Hardy space $H^p_W$, we prove that the dual space of $H^p_W$ is precisely $\\mathcal L_{p,q,s,W}$, which further induces several equivalent characterizations of $\\mathcal L_{p,q,s,W}$. In addition, we ob"},"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":"2508.15195","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-08-21T03:08:04Z","cross_cats_sorted":["math.AP","math.CA"],"title_canon_sha256":"86909f1239d0c095deca367863fe7b636b7743d10d3c0a71a4a0e0df965126c3","abstract_canon_sha256":"f91a62168addee9b1408c9707cab1f6877aed4cd0058dfbf7c8501a743ffad43"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:57:08.100400Z","signature_b64":"dc5FTM2KP03vaZx0L8xhQnTFCeGJc8OTL5mv1SJFBwtcQfoIjvQPK6dLat3/ZmVwBdUCbtqVBmE3lbHODeUbBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4694c12a2e925415ad6d6d3e7b995aae4bbbe1552fdd25cd6bb630692990d613","last_reissued_at":"2026-07-05T11:57:08.099989Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:57:08.099989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matrix-Weighted Campanato Spaces: Duality and Calder\\'on--Zygmund Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.FA","authors_text":"Dachun Yang, Wen Yuan, Yiqun Chen","submitted_at":"2025-08-21T03:08:04Z","abstract_excerpt":"Let $p\\in(0,\\infty)$, $q\\in[1,\\infty)$, $s\\in\\mathbb Z_+$, and $W$ be an $A_p$-matrix weight, which in the scalar case is exactly a Muckenhoupt $A_{\\max\\{1,p\\}}$ weight. In this article, by using the reducing operators of $W$, we introduce matrix-weighted Campanato spaces $\\mathcal L_{p,q,s,W}$. When $p\\in(0,1]$, applying the atomic and the finite atomic characterizations of the matrix-weighted Hardy space $H^p_W$, we prove that the dual space of $H^p_W$ is precisely $\\mathcal L_{p,q,s,W}$, which further induces several equivalent characterizations of $\\mathcal L_{p,q,s,W}$. 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