A Classification Theorem on Non-compact Embeddings between Besov Spaces

2024/10/14 by Chian Yeong Chuah, Chuah, Chian Yeong, Ján Lang +3
Mathematics · #47B06 (primary) 46E35 and 46B45 (secondary) #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2410.10731

openalex publication_date 2024/10/14 · openalex created_date 2024/10/20 · openalex updated_date 2026/07/28

Abstract

We analyze the embedding properties between Besov spaces, defined on the total space \mathbb Rⁿ and on bounded domains. We give a complete classification on whether or not these embedding maps satisfy certain weak compactness characterized by the so-called strictly and finitely strictly singular condition. The result extends the recent findings on Sobolev embeddings by offering a refined description of the quality of non-compactness in the setting of Besov spaces.

Related

• Compact embeddings in Besov-type and Triebel-Lizorkin-type Spaces on\n bounded domains
• Non-collapsing condition and Sobolev embeddings for Hajłasz-Besov spaces
• Embeddings for anisotropic Besov spaces
• Quality of non-compactness for Sobolev Embedding with one point non-compactness
• Besov classes on finite- and infinite-dimensional spaces and embedding\n theorems