论文标题
莫里序列空间和光滑度莫雷空间的核嵌入
Nuclear embeddings of Morrey sequence spaces and smoothness Morrey spaces
论文作者
论文摘要
我们研究了Morrey类型空间的核嵌入，无论是在其序列空间版本中还是作为在有限域$ω\ subset {\ Mathbb r}^d $上定义的函数的平滑度空间。这尤其涵盖了同时，在有限的域上定义的Besov和Triebel-Lizorkin型空间的知名且完全回答的情况，这已被考虑了很长时间。完整的结果仅是最近才获得的。已经详细研究了莫雷类型功能空间的紧凑型嵌入，还涉及它们的熵和近似数。现在，我们在这种情况下证明了第一个完全完全的核性结果。 Grothendieck在1955年已经引入了核性的概念。再次，我们依靠合适的小波分解技术和著名的TONG结果（1969年），其特征是核对角算子在$ \ ell_r $类型的序列空间之间作用，$ \ ell_r $ type，$ 1 \ leq leq r \ leq r \ leq \ leq \ infty $。
We study nuclear embeddings for spaces of Morrey type, both in its sequence space version and as smoothness spaces of functions defined on a bounded domain $Ω\subset {\mathbb R}^d$. This covers, in particular, the meanwhile well-known and completely answered situation for spaces of Besov and Triebel-Lizorkin type defined on bounded domains which has been considered for a long time. The complete result was obtained only recently. Compact embeddings for function spaces of Morrey type have already been studied in detail, also concerning their entropy and approximation numbers. We now prove the first and complete nuclearity result in this context. The concept of nuclearity has already been introduced by Grothendieck in 1955. Again we rely on suitable wavelet decomposition techniques and the famous Tong result (1969) which characterises nuclear diagonal operators acting between sequence spaces of $\ell_r$ type, $1 \leq r \leq\infty$.
