Generalized Levy representation of norms and isometric embeddings into \(L_ p\)-spaces
type: Item
instance of: scholarly article
title: Generalized Levy representation of norms and isometric embeddings into \(L_ p\)-spaces
zbMATH Open document ID: 0766.46009
author: Alexander Koldobsky
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1993-01-17T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77435
review text: The author proves that if \(p>0\), \(p\neq 2,4,6,\dots\) then the norm of every \(n\)-dimensional Banach space admits a representation \[ \| x\|^ p=\int_{\mathbb{R}^ N}|\langle x,s\rangle|^ pd\gamma(s), \] where \(\gamma\) is a distribution. This representation is used in order to obtain criteria for isometric embeddability of Banach spaces into \(L_ p\) spaces.
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 97821
zbMATH Keywords: Fourier transform
zbMATH Keywords: criteria for isometric embeddability of Banach spaces into \(L_ p\) spaces
zbMATH Keywords: distribution
zbMATH Keywords: representation
reviewed by: Mikhail Ostrovskii
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 97821