Extension of vector-valued functions and weak-strong principles for differentiable functions of finite order

Publikationstyp
Journal Article
Publikationsdatum
2022-01
Sprache
English
Author
Kruse, Karsten orcid-logo
Institut
Mathematik E-10 
DOI
10.15480/882.4017
TORE-URI
http://hdl.handle.net/11420/11248
Enthalten in
Annals of functional analysis 
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
10.1007/s43034-021-00154-5
Scopus ID
2-s2.0-85120870776
ArXiv ID
1910.01952
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.
Schlagworte
extension
vector-valued
epsilon-product
weight
weak-strong principle
DDC Class
510: Mathematik
Projekt(e)
Projekt DEAL 
Publication version
publishedVersion
Lizenz
https://creativecommons.org/licenses/by/4.0/
Thumbnail Image
Name

Kruse, Extension of vector-valued functions and weak-strong principles for differentiable functions of finite.pdf

Size

1.75 MB

Format

Adobe PDF