Matrix-weighted Besov–Triebel–Lizorkin spaces of optimal scale: Real-variable characterizations, invariance on integrable index, and Sobolev-type embedding

Key Points

• Matrix-weighted Besov and Triebel-Lizorkin spaces provide a new framework for analysis, focusing on optimal scale.
• Key properties include real-variable characterizations and invariance related to the integrable index.
• The study highlights Sobolev-type embeddings, emphasizing their role in function space theory.
• These findings suggest deeper relationships between various functional spaces, opening new theoretical pathways.