论文标题
对Laakso图的分析，并应用于运输成本空间的结构
Analysis on Laakso graphs with application to the structure of transportation cost spaces
论文作者
论文摘要
本文是我们在[CANAD中的文章的延续。 J. Math。卷。 72（3），（2020），第774---804页。我们构建了循环的正交基础，并缩短了Laakso图的空间$ \ MATHCAL {L} _n $。它们用于分析从边缘空间到周期空间的投影，并获得$ \ operatatorName {Lip} _0（\ Mathcal {l} _N）$的投影常数的合理锐利估计，Lipschitz的空间在$ \ nathcal {l} _n $上函数。我们推断出Banach-Mazur距离Tc $（\ Mathcal {l} _n）$的距离，$ \ Mathcal {l} _n $的运输成本空间到相同维度的$ \ ell_1^n $至少是$（3N-5）/8 $，这是来自[OP的类似物。引用]对于钻石图$ d_n $。我们计算$ \ operatatorName {lip} _0（d_ {n，k}）$的确切投影常数，其中$ d_ {n，k} $是分支$ k $的钻石图。我们还提供了有限度量空间的简单示例，其中包含$ \ ell_ \ infty^3 $和$ \ ell_ \ elfty^4 $的运输成本空间。
This article is a continuation of our article in [Canad. J. Math. Vol. 72 (3), (2020), pp. 774--804]. We construct orthogonal bases of the cycle and cut spaces of the Laakso graph $\mathcal{L}_n$. They are used to analyze projections from the edge space onto the cycle space and to obtain reasonably sharp estimates of the projection constant of $\operatorname{Lip}_0(\mathcal{L}_n)$, the space of Lipschitz functions on $\mathcal{L}_n$. We deduce that the Banach-Mazur distance from TC$(\mathcal{L}_n)$, the transportation cost space of $\mathcal{L}_n$, to $\ell_1^N$ of the same dimension is at least $(3n-5)/8$, which is the analogue of a result from [op. cit.] for the diamond graph $D_n$. We calculate the exact projection constants of $\operatorname{Lip}_0(D_{n,k})$, where $D_{n,k}$ is the diamond graph of branching $k$. We also provide simple examples of finite metric spaces, transportation cost spaces on which contain $\ell_\infty^3$ and $\ell_\infty^4$ isometrically.
