This is an announcement for the paper "Embeddability of snowflaked metrics with applications to the nonlinear geometry of the spaces $L_p$ and $\ell_{p}$ for $0<p<\infty$" by Fernando Albiac and Florent Baudier.

Abstract: We study the classical spaces $L_{p}$ and $\ell_{p}$ for the whole range $0<p<\infty$ from a metric viewpoint and give a complete Lipschitz embeddability roadmap between any two of those spaces when equipped with both their ad-hoc distances and their snowflakings. Through connections with weaker forms of embeddings that lead to basic (yet fundamental) open problems, we also set the challenging goal of understanding the dissimilarities between the well-known subspace structure and the different nonlinear geometries that coexist inside $L_{p}$ and $\ell_{p}$.

Archive classification: math.MG math.FA

Mathematics Subject Classification: 46B80, 46A16, 46T99

Remarks: 25 pages

Submitted from: florent@math.tamu.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1206.3774

or

http://arXiv.org/abs/1206.3774