This research introduces matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces, revealing their norms and implications for boundedness of pseudo-differential operators.
We introduce the homogeneous (inhomogeneous) matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces and obtain equivalent norms of these spaces. 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.
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Bai et al. (2025) studied this question.
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