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arXiv · 2504.19060

Matrix-Weighted Besov--Triebel--Lizorkin Spaces of Optimal Scale: Boundedness of Pseudo-Differential, Trace, and Calder\'{o}n--Zygmund Operators

Dachun Yang·Wen Yuan·Mingdong Zhang
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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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Dachun Yang, Wen Yuan, Mingdong Zhang. 2025-04-27. Matrix-Weighted Besov--Triebel--Lizorkin Spaces of Optimal Scale: Boundedness of Pseudo-Differential, Trace, and Calder\'{o}n--Zygmund Operators. https://arxiv.org/abs/2504.19060

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