论文标题
在有限域中的BESOV型和Triebel-lizorkin型空间中的紧凑型嵌入
Compact embeddings in Besov-type and Triebel-Lizorkin-type Spaces on bounded domains
论文作者
论文摘要
我们研究besov-type和triebel-lizorkin-type空间的嵌入，$id_τ：{b} _ {p_1，q_1}^{s_1，τ_1，τ_1}（ω） {f} _ {p_1，q_1}^{s_1，τ_1}（ω）\ hookrightArrow {f} _ {p_2，q_2}^{s_2，s_2，τ_2，τ_2}（ω）（ω）$ $id_τ$。此外，我们表征其熵和近似数。令人惊讶的是，这些结果是通过嵌入完全获得的，并应用了古典BESOV和Triebel-Lizorkin空间以及Besov-Morrey和Triebel-Lizorkin-Morrey空间的相应结果。
We study embeddings of Besov-type and Triebel-Lizorkin-type spaces, $id_τ: {B}_{p_1,q_1}^{s_1,τ_1}(Ω) \hookrightarrow {B}_{p_2,q_2}^{s_2,τ_2}(Ω)$ and $id_τ: {F}_{p_1,q_1}^{s_1,τ_1}(Ω) \hookrightarrow {F}_{p_2,q_2}^{s_2,τ_2}(Ω) $, where $Ω\subset {\mathbb R}^d$ is a bounded domain, and obtain necessary and sufficient conditions for the compactness of $id_τ$. 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.
