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arXiv · 2109.12015

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

Helena F. Goncalves·Dorothee D. Haroske·Leszek Skrzypczak
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Abstract

In this paper, we study limiting embeddings of Besov-type and Triebel-Lizorkin-type spaces, $id_τ: B_{p_1,q_1}^{s_1,τ_1}(Ω) \rightarrow B_{p_2,q_2}^{s_2,τ_2}(Ω)$ and $id_τ: F_{p_1,q_1}^{s_1,τ_1}(Ω) \rightarrow F_{p_2,q_2}^{s_2,τ_2}(Ω)$, where $Ω\subset \mathbb{R}^d$ 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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Helena F. Goncalves, Dorothee D. Haroske, Leszek Skrzypczak. 2021-10-04. Limiting embeddings of Besov-type and Triebel-Lizorkin-type spaces on domains and an extension operator. https://arxiv.org/abs/2109.12015

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