当重新审视$q>2$时，$\ell_q$的双倍子集没有降维
No dimension reduction for doubling subsets of $\ell_q$ when $q>2$ revisited
摘要：
我们回顾了\cites{BGN_SoCG14,BGN_SIAM15}和\cite{LafforgueNaor14_GD}关于$q>2$的$\ell_q$的加倍子集的维数降低的不可能性的主要结果。我们提供了一个替代的基本证明，这是不可能的结果，结合了简单的建设在\cites{BGN_SoCG14,BGN_SIAM15}与一般性的方法在\cite{LafforgueNaor14_GD}（除了$L_1$的目标）。这种不同的方法的一个优点是，它可以很自然地推广到获得嵌入性障碍到非正曲空间或渐近一致凸巴拿赫空间。
英文摘要：
We revisit the main results from \cites{BGN_SoCG14,BGN_SIAM15} and \cite{LafforgueNaor14_GD} about the impossibility of dimension reduction for doubling subsets of $\ell_q$ for $q>2$. We provide an alternative elementary proof of this impossibility result that combines the simplicity of the construction in \cites{BGN_SoCG14,BGN_SIAM15} with the generality of the approach in \cite{LafforgueNaor14_GD} (except for $L_1$ targets). One advantage of this different approach is that it can be naturally generalized to obtain embeddability obstructions into non-positively curved spaces or asymptotically uniformly convex Banach spaces.
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