Matrix-weighted Campanato spaces: duality and Calderón-Zygmund operators

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发表日期：

2026年8月5日

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Yiqun Chen,
Dachun Yang,
Wen Yuan

摘要

Let p ∈ (0, ∞), q ∈ [1, ∞), and s ∈ ℤ₊, and let 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 ℒ_p,q,s,W. When p ∈ (0,1], applying the atomic and the finite atomic characterizations of the matrix-weighted Hardy space H _W ^p , we prove that the dual space of H _W ^p is precisely ℒ_p,q,s,W, which further induces several equivalent characterizations of ℒ_p,q,s,W. In addition, we obtain a necessary and sufficient condition for the boundedness of modified Calderón-Zygmund operators on ℒ_p,q,s,W with p ∈ (0, ∞), which, combined with the duality, further gives a necessary and sufficient condition for the boundedness of Calderón-Zygmund operators on H _W ^p with p ∈ (0,1].