On matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911336655486976 |
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| author | Bai, Tengfei Guo, Pengfei Xu, Jingshi |
| author_facet | Bai, Tengfei Guo, Pengfei Xu, Jingshi |
| contents | 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 $g_λ^{*}$-function, approximation, wavelet and atom. As an application, we obtain boundedness of pseudo-differential operators with symbols in the Hörmander classes and Hölder-Zygmund classes on inhomogeneous matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_11981 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces Bai, Tengfei Guo, Pengfei Xu, Jingshi Functional Analysis Classical Analysis and ODEs Primary 42B35, Secondary 46E30, 42B25, 42B20, 42C40, 35S05 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 $g_λ^{*}$-function, approximation, wavelet and atom. As an application, we obtain boundedness of pseudo-differential operators with symbols in the Hörmander classes and Hölder-Zygmund classes on inhomogeneous matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces. |
| title | On matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces |
| topic | Functional Analysis Classical Analysis and ODEs Primary 42B35, Secondary 46E30, 42B25, 42B20, 42C40, 35S05 |
| url | https://arxiv.org/abs/2508.11981 |