Quantitative nonlinear embeddings into Lebesgue sequence spaces

Abstract

In this paper fundamental nonlinear geometries of Lebesgue sequence spaces are studied in their quantitative aspects. Applications of this work are a positive solution to the strong embeddability problem from ${\ell }_q$ into ${\ell }_p$ ($0<p<q\le 1$) and new insights on the coarse embedabbility problem from $L_q$ into ${\ell }_q$, $q>2$. Relevant to geometric group theory purposes, the exact ${\ell }_p$-compressions of ${\ell }_2$ are computed. Finally coarse deformation of metric spaces with property A and locally compact amenable groups is investigated.

34 pages

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• Euclidean quotients of finite metric spaces
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Cited by in corpus (3)

• The coarse geometry of Tsirelson's space and applications
• An average John theorem
• Tight embeddability of proper and stable metric spaces