The dual of the matrix-weighted Hardy space H^p_W is the newly defined matrix-weighted Campanato space L_{p,q,s,W}, and Calderón-Zygmund operators act boundedly exactly when they annihilate polynomials up to order s.
Matrix-Weighted Besov--Triebel--Lizorkin Spaces of Optimal Scale: Boundedness of Pseudo-Differential, Trace, and Calder\'{o}n--Zygmund Operators
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abstract
This article is a continuation of our work on generalized matrix-weighted Besov--Triebel--Lizorkin-type spaces with matrix $\mathcal{A}_{\infty}$ weights. In this article, we establish the boundedness of pseudo-differential, trace, and Calder\'{o}n--Zygmund operators on these spaces. The main tools involved in this article are the molecular and the wavelet characterizations of these spaces. Since generalized matrix-weighted Besov--Triebel--Lizorkin-type spaces include many classical function spaces such as matrix-weighted Besov--Triebel--Lizorkin spaces, all the results in this article are of wide generality.
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Matrix-Weighted Campanato Spaces: Duality and Calder\'on--Zygmund Operators
The dual of the matrix-weighted Hardy space H^p_W is the newly defined matrix-weighted Campanato space L_{p,q,s,W}, and Calderón-Zygmund operators act boundedly exactly when they annihilate polynomials up to order s.