On Whitney-type extension theorems on Banach spaces for C1,ω,C1,+, C1,+ loc , and C1,+ B-smooth functions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10492731" target="_blank" >RIV/00216208:11320/24:10492731 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=x.D22UrU_P" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=x.D22UrU_P</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2023.127976" target="_blank" >10.1016/j.jmaa.2023.127976</a>
Alternative languages
Result language
angličtina
Original language name
On Whitney-type extension theorems on Banach spaces for C1,ω,C1,+, C1,+ loc , and C1,+ B-smooth functions
Original language description
Our paper is a complement to a recent article by D. Azagra and C. Mudarra (2021, [2]). We show how older results on semiconvex functions with modulus omega easily imply extension theorems for C1,omega-smooth functions on super-reflexive Banach spaces which are versions of some theorems of Azagra and Mudarra. We present also some new interesting consequences which are not mentioned in their article, in particular extensions of C1,omega-smooth functions from open quasiconvex sets. They proved also an extension theorem for C1,+ B-smooth functions (i.e., functions with uniformly continuous derivative on each bounded set) on Hilbert spaces. Our version of this theorem and new extension results for C1,+ and C1,+ loc-smooth functions (i.e., functions with uniformly, resp. locally uniformly continuous derivative), all of which are proved on arbitrary super-reflexive Banach spaces, are further main contributions of our paper. Some of our proofs use main ideas of the article by D. Azagra and C. Mudarra, but all are formally completely independent on their article. (c) 2023 Elsevier Inc. All rights reserved.
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
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
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 Mathematical Analysis and Applications
ISSN
0022-247X
e-ISSN
1096-0813
Volume of the periodical
532
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
27
Pages from-to
127976
UT code for WoS article
001125488400001
EID of the result in the Scopus database
2-s2.0-85177999921