Matrix-weighted Besov-Triebel-Lizorkin spaces with logarithmic smoothness

In this article, the authors study the matrix -weighted Besov- Triebel-Lizorkin spaces with logarithmic smoothness. Via first obtaining the L p ( R n )-boundedness and the Fefferman- Stein type vector -valued inequality of matrix -weighted Peetretype maximal functions with the exquisite ranges of indices in terms of the A p dimension of matrix weights under consideration, the authors establish an equivalent characterization of these spaces in terms of the matrix -weighted Peetretype maximal functions, which further implies that these spaces are well defined. As an application, the authors obtain the boundedness of some pointwise multipliers on these spaces and, even back to classical Besov-Triebel-Lizorkin spaces, some of them are also new. (c) 2024 Elsevier Masson SAS. All rights are reserved, including those for text and data mining, AI training, and similar technologies.