Smoothing of uniformly continuous mappings in \(L_ p\) spaces
type: Item
instance of: scholarly article
title: Smoothing of uniformly continuous mappings in \(L_ p\) spaces
zbMATH Open document ID: 0821.46037
DOI: 10.1007/BF01209562
author: Igor G. Tsar'kov
published in: Mathematical Notes
publication date: 1994-11-16T00:00:00Z
review text: The paper deals with approximation of uniformly continuous mappings of the unit ball \(B_ p\subset L_ p\) into \(L_ q\) by functions from Hölder classes. For spaces defined on a measure space with a \(\sigma\)- additive measure, lower bounds for the Hölder exponent are established and a quantitative dependence on further geometric properties is studied (general Banach spaces, uniformly convex spaces, superreflexive spaces). The Hölder exponents are shown to be the best for \(L_ p\) spaces on the real line.
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 687511
zbMATH Keywords: Hölder continuity
zbMATH Keywords: approximation of uniformly continuous mappings
zbMATH Keywords: Hölder classes
zbMATH Keywords: Hölder exponent
zbMATH Keywords: uniformly convex spaces
zbMATH Keywords: superreflexive spaces
reviewed by: Miroslav Krbec
MaRDI profile type: Publication
cites work: A Lipschitz Condition Preserving Extension for a Vector Function
cites work: Q3843864
cites work: Q5583225
cites work: On the extension of Lipschitz-Hölder maps on $L^{P}$ spaces
full work available at URL: https://doi.org/10.1007/bf01209562
OpenAlex ID: W2083611744
description: scientific article; zbMATH DE number 687511