Improved bounds in the metric cotype inequality for Banach spaces

Title: Improved bounds in the metric cotype inequality for Banach spaces
Creator: Giladi, Ohad; Mendel, Manor; Naor, Assaf
Relation: Journal of Functional Analysis Vol. 260, Issue 1, p. 164-194
Publisher Link: http://dx.doi.org/10.1016/j.jfa.2010.08.015
Publisher: Academic Press
Resource Type: journal article
Date: 2011
Description: It is shown that if (X,||·||X) is a Banach space with Rademacher cotype q then for every integer n there exists an even integer m≲n ^1+1/q such that for every f:Z n/m → X we have [formula could not be replicated] where the expectations are with respect to uniformly chosen x∈Zn/m and ε∈{-1,0,1}ⁿ, and all the implied constants may depend only on q, and the Rademacher cotype q constant of X. This improves the bound of m≲n^2+1/q from Mendel and Naor (2008). The proof of (1) is based on a "smoothing and approximation" procedure which simplifies the proof of the metric characterization of Rademacher cotype of Mendel and Naor (2008). We also show that any such "smoothing and approximation" approach to metric cotype inequalities must require m≳n ^{1/2 + 1/q}.
Subject: metric cotype; bi-Lipschitz embeddings; coarse embeddings
Identifier: http://hdl.handle.net/1959.13/1356011
Identifier: uon:31587
Identifier: ISSN:0022-1236
Language: eng
Reviewed

		Thumbnail	File	Description	Size	Format