Limiting embeddings of Besov-type and Triebel-Lizorkin-type spaces on domains and an extension operator

2021/09/24 by Helena F. Gonçalves, Goncalves, Helena F., Dorothee D. Haroske +3 · 1 citation
Mathematics · #42B35 #46E35 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2109.12015

openalex publication_date 2021/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study limiting embeddings of Besov-type and Triebel-Lizorkin-type spaces, id_τ: B_p1,q1^s₁,τ₁(Ω) → B_p2,q2^s₂,τ₂(Ω) and id_τ: F_p1,q1^s₁,τ₁(Ω) → F_p2,q2^s₂,τ₂(Ω), where Ω⊂ ℝ^d is a bounded domain, obtaining necessary and sufficient conditions for the continuity of id_τ. This can also be seen as the continuation of our previous studies of compactness of the embeddings in the non-limiting case. Moreover, we also construct Rychkov's linear, bounded universal extension operator for these spaces.

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