Inner structure of non-compact embeddings between Triebel–Lizorkin spaces

Investigate the inner structure of non-compact embeddings between Triebel–Lizorkin spaces, including how their sequence-space representations via wavelet decompositions reflect and govern these embeddings’ properties.

Background

The paper focuses on Besov spaces and uses wavelet decompositions to reduce embedding questions to sequence spaces, enabling a fine classification of non-compact embeddings.

The authors point out that Triebel–Lizorkin spaces have different sequence-space behaviors under wavelet decompositions, which makes their paper more challenging, and explicitly raise the question of understanding the inner structure of non-compact embeddings in that scale.