This is an announcement for the paper "Quantitative nonlinear embeddings into Lebesgue sequence spaces" by Florent P. Baudier.
Abstract: In this paper coarse, uniform and strong embeddings of metric spaces into Lebesgue sequence spaces are studied in their quantitative aspects. In particular, strong deformation gaps are obtained when embedding strongly a Hilbert space into $\ell_p$ for $0<p< 2$ as well as new insights on the nonlinear geometry of the spaces $L_p$ and $\ell_p$ for $0<p<1$. The exact $\ell_q$-compression of $\ell_p$-spaces is computed. Finally the coarse deformation of metric spaces with property A and amenable groups is investigated.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46B20, 46B85, 46T99, 20F65
Submitted from: florent@math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.0588
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