论文标题
关于Chemin均匀分布空间的评论
Remarks on Chemin's space of homogeneous distributions
论文作者
论文摘要
本文重点介绍了Chemin的空间$ \ Mathcal {s}'_ H $均匀分布，该分布被引入是为了实现亚临界均质besov空间的基础。我们将讨论该结构如何以多种方式用于超临界空间。特别是，我们研究其交叉点$ x_h：= \ Mathcal {s}'_ H \ cap x $带有各种Banach Spaces $ X $，即超临界均质besov Space和Lebesgue Space $ L^\ lyfty $。对于每个$ x $，我们找出交叉点$ x_h $在$ x $中的密集。如果不是这样，那么我们研究其关闭$ c = {\ rm clos}（x_h）$，并证明商$ x/c $不可分开，并且$ c $不补充$ x $。
This article focuses on Chemin's space $\mathcal{S}'_h$ of homogeneous distributions, which was introduced to serve as a basis for realizations of subcritical homogeneous Besov spaces. We will discuss how this construction fails in multiple ways for supercritical spaces. In particular, we study its intersection $X_h := \mathcal{S}'_h \cap X$ with various Banach spaces $X$, namely supercritical homogeneous Besov spaces and the Lebesgue space $L^\infty$. For each $X$, we find out if the intersection $X_h$ is dense in $X$. If it is not, then we study its closure $C = {\rm clos}(X_h)$ and prove that the quotient $X/C$ is not separable and that $C$ is not complemented in $X$.
