An inequality for \(L_ p\)-norms with respect to the multivariate normal distribution
type: Item
instance of: scholarly article
title: An inequality for \(L_ p\)-norms with respect to the multivariate normal distribution
zbMATH Open document ID: 0542.60031
DOI: 10.1016/0022-247X(84)90209-9
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: Let X be an \({\mathbb{R}}^ k\)-valued random variable with expectation 0 and with a k-variate normal distribution, \(\| \cdot \|\) a norm in \({\mathbb{R}}^ k\), and \(Y=\| X\|\). The author shows the existence of a constant \(c_ p\) such that \(\| Y\|_ p\leq c_ p\| Y\|_ 1\). His constant is \(c_ p=2((p+1)/2)^{1/p}\pi^{(p-1)/2p}, (1<p<\infty)\).
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 3862137
zbMATH Keywords: Lp-norm
zbMATH Keywords: normal distribution
author: Wolfgang Stadje
reviewed by: Ulrich Krengel
MaRDI profile type: Publication
cites work: Q5336417
cites work: Q5606327
cites work: The dimension of almost spherical sections of convex bodies
cites work: Q5623005
full work available at URL: 0022-247x(84)90209-9
OpenAlex ID: W2085157189
description: scientific article; zbMATH DE number 3862137