矩阵加权各向异性Besov型和Triebel-Lizorkin型空间的等价范数与φ变换
Equivalent norms and $φ$-transform of matrix-weighted anisotropic Besov-type and Triebel-Lizorkin-type spaces
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中文总结 AI 辅助
本文引入与扩张矩阵A相关的矩阵加权各向异性Besov型和Triebel-Lizorkin型空间，利用矩阵权重性质证明其与对应平均空间等价、建立离散φ变换，还研究了p=∞时对应Triebel-Lizorkin空间的φ变换及相关空间关系。
中文摘要 AI 辅助
我们引入了与扩张矩阵A相关的矩阵加权各向异性Besov型和Triebel-Lizorkin型空间。受Bu等人（2025）提出的矩阵权重的A_p维数启发，我们研究了与A相关的矩阵权重的性质。利用矩阵权重的良好性质，我们得到这些空间与其对应的平均空间等价，并建立了这些空间的离散φ变换。最后，我们针对极限情况p=∞引入了矩阵加权各向异性Triebel-Lizorkin空间，并得到其φ变换，同时还研究了该空间与矩阵加权各向异性Besov型和Triebel-Lizorkin型空间之间的关系。
英文摘要
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 $φ$-transform of these spaces. Finally, we introduce matrix-weighted anisotropic Triebel-Lizorkin spaces for the limiting case $p=\infty$ and obtain their $φ$-transform. The relation between matrix-weighted anisotropic Triebel-Lizorkin spaces and matrix-weighted anisotropic Besov-type and Triebel-Lizorkin-type spaces is also studied.
