An extension of the Kahane-Khinchine inequality in a Banach space
type: Item
instance of: scholarly article
title: An extension of the Kahane-Khinchine inequality in a Banach space
zbMATH Open document ID: 0654.46019
DOI: 10.1007/BF02767353
author: David C. Ullrich
published in: Israel Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Let \(\omega_ 1,\omega_ 2,..\). be the Steinhaus variables (independent identically distributed random variables, uniformly distributed on [0,1]) and X a Banach space. Then there is a constant \(c>0\) such that \[ \exp {\mathcal E} \log \| \sum^{N}_{j=1}e^{2\pi i\omega_ j}x_ j\| \geq c({\mathcal E}\| \sum^{N}_{j=1}e^{2\pi i\omega_ j}x_ j\|)^{1/2} \] for any N and \(x_ 1,...,x_ N\) in X, where \({\mathcal E}\) denotes the expected value.
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B42
zbMATH DE Number: 4067598
zbMATH Keywords: Kahane-Khinchine inequality
zbMATH Keywords: Steinhaus variables
zbMATH Keywords: independent identically distributed random variables
MaRDI profile type: Publication
cites work: Q5587572
cites work: Isomorphic characterizations of inner product spaces by orthogonal series with vector valued coefficients
cites work: Q4188284
description: scientific article; zbMATH DE number 4067598