Convex integrals of molecules in Lipschitz-free spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F24%3A00377295" target="_blank" >RIV/68407700:21240/24:00377295 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jfa.2024.110560" target="_blank" >https://doi.org/10.1016/j.jfa.2024.110560</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2024.110560" target="_blank" >10.1016/j.jfa.2024.110560</a>
Alternative languages
Result language
angličtina
Original language name
Convex integrals of molecules in Lipschitz-free spaces
Original language description
We introduce convex integrals of molecules in Lipschitz-free spaces F(M) as a continuous counterpart of convex series considered elsewhere, based on the de Leeuw representation. Using optimal transport theory, we show that these elements are determined by cyclical monotonicity of their supports, and that under certain finiteness conditions they agree with elements of F(M) that are induced by Radon measures on M, or that can be decomposed into positive and negative parts. We also show that convex integrals differ in general from convex series of molecules. Finally, we present some standalone results regarding extensions of Lipschitz functions which, combined with the above, yield applications to the extremal structure of F(M). In particular, we show that all elements of F(M) are convex series of molecules when M is uniformly discrete and identify all extreme points of the unit ball of F(M) in that case.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA22-32829S" target="_blank" >GA22-32829S: The structure of free Banach spaces and of their second duals</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
JOURNAL OF FUNCTIONAL ANALYSIS
ISSN
0022-1236
e-ISSN
1096-0783
Volume of the periodical
287
Issue of the periodical within the volume
8
Country of publishing house
US - UNITED STATES
Number of pages
43
Pages from-to
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UT code for WoS article
001268845100001
EID of the result in the Scopus database
2-s2.0-85198077144