On matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces

TL;DR

This paper introduces new matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces, provides their equivalent norms and characterizations, and demonstrates boundedness of certain pseudo-differential operators on these spaces.

Contribution

It defines and characterizes matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces, extending the theory and applying it to operator boundedness.

Findings

Established equivalent norms for the new spaces

Provided characterizations via maximal functions and wavelets

Proved boundedness of pseudo-differential operators

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.