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arXiv · 2508.11981

On matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces

Tengfei Bai·Pengfei Guo·Jingshi Xu
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Abstract

We introduce the homogeneous (inhomogeneous) matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces and obtain their equivalent norms. We also obtain their characterizations by Peetre type maximal functions, Lusin-area function, Littlewood-Paley $g_{\lambda}^{*}$-function, approximation, wavelet and atom. As an application, we obtain boundedness of pseudo-differential operators with symbols in the H\"{o}rmander classes and H\"{o}lder-Zygmund classes on inhomogeneous matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces.

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Tengfei Bai, Pengfei Guo, Jingshi Xu. 2025-08-16. On matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces. https://arxiv.org/abs/2508.11981

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