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Extension of vector-valued functions and weak-strong principles for differentiable functions of finite order
Citation Link: https://doi.org/10.15480/882.4017
Publikationstyp
Journal Article
Date Issued
2022-01
Sprache
English
Author(s)
Institut
TORE-DOI
Journal
Volume
13
Issue
1
Start Page
1
End Page
26
Article Number
10
Citation
Annals of Functional Analysis 13 (1): 1-26 (2022-02)
Publisher DOI
Scopus ID
ArXiv ID
Publisher
Springer International Publishing
Peer Reviewed
true
In this paper we study the problem of extending functions with values in a locally convex Hausdorff space E over a field K, which has weak extensions in a weighted Banach space Fν(Ω,K) of scalar-valued functions on a set Ω, to functions in a vector-valued counterpart Fν(Ω,E) of Fν(Ω,K). Our findings rely on a description of vector-valued functions as continuous linear operators and extend results of Frerick, Jordá and Wengenroth. As an application we derive weak-strong principles for continuously partially differentiable functions of finite order and vector-valued versions of Blaschke’s convergence theorem for several spaces.
Subjects
extension
vector-valued
epsilon-product
weight
weak-strong principle
DDC Class
510: Mathematik
Publication version
publishedVersion
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Name
Kruse, Extension of vector-valued functions and weak-strong principles for differentiable functions of finite.pdf
Size
1.75 MB
Format
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