Improved bounds in the metric cotype inequality for Banach spaces

Ohad Giladi, Manor Mendel, Assaf Naor

Research output: Contribution to journalArticle

Abstract

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 m n→X we have. where the expectations are with respect to uniformly chosen x∈Z m n 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≲n2+1q from Mendel and Naor (2008) [13]. 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) [13]. We also show that any such "smoothing and approximation" approach to metric cotype inequalities must require m≳n 1/2 + 1/q.

Original languageEnglish (US)
Pages (from-to)164-194
Number of pages31
JournalJournal of Functional Analysis
Volume260
Issue number1
DOIs
StatePublished - Jan 1 2011

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Smoothing
Banach space
Metric
Integer
Approximation
Simplify

Keywords

  • Bi-Lipschitz embeddings
  • Coarse embeddings
  • Metric cotype

ASJC Scopus subject areas

  • Analysis

Cite this

Improved bounds in the metric cotype inequality for Banach spaces. / Giladi, Ohad; Mendel, Manor; Naor, Assaf.

In: Journal of Functional Analysis, Vol. 260, No. 1, 01.01.2011, p. 164-194.

Research output: Contribution to journalArticle

Giladi, Ohad ; Mendel, Manor ; Naor, Assaf. / Improved bounds in the metric cotype inequality for Banach spaces. In: Journal of Functional Analysis. 2011 ; Vol. 260, No. 1. pp. 164-194.
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