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Abstract <p> This article is a continuation of our work on generalized matrix-weighted Besov–Triebel–Lizorkin-type spaces with matrix <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal A_\infty\)</EquationSource> </InlineEquation> 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 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. </p>

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

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Dachun Yang,
  • Wen Yuan,
  • Mingdong Zhang

摘要

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 Calderón–Zygmund operators on these spaces. The main tools involved in this article are the molecular and 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.