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arXiv · 2001.02046

Compact embeddings in Besov-type and Triebel-Lizorkin-type Spaces on bounded domains

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

We study embeddings of Besov-type and Triebel-Lizorkin-type spaces, $id_\tau : {B}_{p_1,q_1}^{s_1,\tau_1}(\Omega) \hookrightarrow {B}_{p_2,q_2}^{s_2,\tau_2}(\Omega)$ and $id_\tau : {F}_{p_1,q_1}^{s_1,\tau_1}(\Omega) \hookrightarrow {F}_{p_2,q_2}^{s_2,\tau_2}(\Omega) $, where $\Omega \subset {\mathbb R}^d$ is a bounded domain, and obtain necessary and sufficient conditions for the compactness of $id_\tau$. Moreover, we characterise its entropy and approximation numbers. Surprisingly, these results are completely obtained via embeddings and the application of the corresponding results for classical Besov and Triebel-Lizorkin spaces as well as for Besov-Morrey and Triebel-Lizorkin-Morrey spaces.

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Helena F. Gonçalves, Dorothee D. Haroske, Leszek Skrzypczak. 2020-01-07. Compact embeddings in Besov-type and Triebel-Lizorkin-type Spaces on bounded domains. https://arxiv.org/abs/2001.02046

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