标题： 关于矩阵加权Bourgain-Morrey Triebel-Lizorkin空间 显示英文标题

标题： On matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces

摘要： 我们引入了齐次（非齐次）矩阵加权Bourgain-MorreyTriebel-Lizorkin空间，并获得了这些空间的等价范数。我们也通过Peetre型最大函数、Lusin面积函数、Littlewood-Paley$g_{\lambda}^{*}$函数、逼近、小波和原子对其进行了表征。作为应用，我们得到了符号属于Hörmander类和Hölder-Zygmund类的伪微分算子在非齐次矩阵加权Bourgain-MorreyTriebel-Lizorkin空间上的有界性。 显示英文摘要

摘要： 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 $g_{\lambda}^{*}$-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.