2025/05/04 by Fan Bu, Dachun Yang, Bu, Fan +5 · 1 citation
Mathematics · #42B25 #42B35 #42C40 #46E40 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #Nonlinear Partial Differential Equations #Primary 46E35 #Secondary 47A56
paper · pdf · doi:10.48550/arxiv.2505.02136
openalex publication_date 2025/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, using growth functions we introduce generalized matrix-weighted Besov-Triebel-Lizorkin-type spaces with matrix A∞ weights. We first characterize these spaces, respectively, in terms of the φ-transform, the Peetre-type maximal function, and the Littlewood-Paley functions. Furthermore, after establishing the boundedness of almost diagonal operators on the corresponding sequence spaces, we obtain the molecular and the wavelet characterizations of these spaces. As applications, we find the sufficient and necessary conditions for the invariance of those Triebel-Lizorkin-type spaces on the integrable index and also for the Sobolev-type embedding of all these spaces. The main novelty exists in that these results are of wide generality, the growth condition of growth functions is not only sufficient but also necessary for the boundedness of almost diagonal operators and hence this new framework of Besov-Triebel-Lizorkin-type is optimal, some results either are new or improve the known ones even for known matrix-weighted Besov-Triebel-Lizorkin spaces, and, furthermore, even in the scalar-valued setting, all the results are also new.