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arXiv · 2608.14237

Equivalent norms and $\varphi$-transform of matrix-weighted anisotropic Besov-type and Triebel-Lizorkin-type spaces

Tengfei Bai·Pengfei Guo·Jingshi Xu
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Abstract

We introduce matrix-weighted anisotropic Besov-type and Triebel-Lizorkin-type spaces associated with an expansive matrix $A$. Inspired by the $\A_p$-dimensions of matrix weight of Bu et al. (2025), we study the properties of matrix weight associated with $A$. Using the nice properties of matrix weight, we obtain that these spaces are equivalent with their corresponding averaging spaces and establish the discrete $\varphi$-transform of these spaces. Finally, we introduce matrix-weighted anisotropic Triebel-Lizorkin spaces for the limiting case $p=\infty$ and obtain their $\varphi$-transform. The relation between matrix-weighted anisotropic Triebel-Lizorkin spaces and matrix-weighted anisotropic Besov-type and Triebel-Lizorkin-type spaces is also studied.

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Tengfei Bai, Pengfei Guo, Jingshi Xu. 2026-08-14. Equivalent norms and $\varphi$-transform of matrix-weighted anisotropic Besov-type and Triebel-Lizorkin-type spaces. https://arxiv.org/abs/2608.14237

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