Clarkson's inequalities, Besov spaces and Triebel-Sobolev spaces
type: Item
instance of: scholarly article
title: Clarkson's inequalities, Besov spaces and Triebel-Sobolev spaces
zbMATH Open document ID: 0663.46026
DOI: 10.4171/ZAA/300
author: Fernando Cobos
author: D. E. Edmunds
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1988-01-01T00:00:00Z
review text: Carkson's inequalities in \(L_ p\) are generalizations of the parallelogram law in \(L_ 2\). They also show that \(L_ p\) is uniformly convex for p greater than one. The present note shows that the same inequalities hold in some Besov spaces and Triebel-Sobolev spaces. The proof is based on the computation of the type or cotype constants of certain of those spaces. The Clarkson inequalities then follow immediately provided a suitable \(L_ r\)-norm is chosen by the definition of the Radamacher type or cotype.
reviewed by: J.Madjarova
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 4084332
zbMATH Keywords: Carkson's inequalities in \(L_ p\)
zbMATH Keywords: parallelogram law
zbMATH Keywords: Besov spaces
zbMATH Keywords: Triebel-Sobolev spaces
zbMATH Keywords: computation of the type or cotype constants
zbMATH Keywords: Radamacher type or cotype
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/300
OpenAlex ID: W2566798103
description: scientific article; zbMATH DE number 4084332