This is an announcement for the paper “On embeddings of locally finite metric spaces into $\ell_p$” by Sofiya Ostrovskahttps://arxiv.org/find/math/1/au:+Ostrovska_S/0/1/0/all/0/1, Mikhail I. Ostrovskiihttps://arxiv.org/find/math/1/au:+Ostrovskii_M/0/1/0/all/0/1.
Abstract: It is known that if finite subsets of a locally finite metric space $M$ admit $C$-bilipschitz embeddings into $\ell_p$ $(1\leq p\leq\infty)$, then for every $\epsilon>0$, the space $M$ admits a $C+\epsilon$-bilipschitz embedding into $\ell_p$. The goal of this paper is to show that for $p\neq 2, \infty$ this result is sharp in the sense that ϵ cannot be dropped out of its statement.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1712.08255