Matrix-Weighted Besov--Triebel--Lizorkin Spaces of Optimal Scale: Boundedness of Pseudo-Differential, Trace, and Calderón--Zygmund Operators

This article is a continuation of our work on generalized matrix-weighted Besov–Triebel–Lizorkin-type spaces with matrix ${\mathcal{A}}_{\mathrm{\infty }}$ weights. In this article, we establish the boundedness of pseudo-differential, trace, and Calderón–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.