论文标题
关于Laakso空间的概述
An Overview on Laakso Spaces
论文作者
论文摘要
Laakso的建筑是AHLFORS $ Q $定型度量空间的著名例子，承认薄弱的$（1,1）$ - Poincaré不平等，无法将任何$ n $嵌入$ \ Mathbb {r}^n $中。该构建特别令人感兴趣，因为它适用于任何固定尺寸$ q> 1 $，甚至是分数。在本文中，我们将通过扩大他的一些陈述并证明原始论文中未经证实的结果来阐明Laakso的作品。
Laakso's construction is a famous example of an Ahlfors $Q$-regular metric measure space admitting a weak $(1,1)$-Poincaré inequality that can not be embedded in $\mathbb{R}^n$ for any $n$. The construction is of particular interest because it works for any fixed dimension $Q>1$, even fractional ones. In this paper we will shed some light on Laakso's work by expanding some of his statements and proving results that were left unproved in the original paper.
