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Publisher DOI: 10.1007/s43034-021-00154-5
arXiv ID: 1910.01952
Title: Extension of vector-valued functions and weak-strong principles for differentiable functions of finite order
Language: English
Authors: Kruse, Karsten  
Keywords: extension; vector-valued; epsilon-product; weight; weak-strong principle
Issue Date: 6-Dec-2021
Publisher: Springer International Publishing
Source: Annals of Functional Analysis 13 (1): 1-26 (2021-12-06)
Abstract (english): 
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.
DOI: 10.15480/882.4017
ISSN: 2008-8752
Journal: Annals of functional analysis 
Institute: Mathematik E-10 
Document Type: Article
Project: Projekt DEAL 
More Funding information: Open Access funding enabled and organized by Projekt DEAL.
Peer Reviewed: Yes
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
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