On Whitney-type extension theorems on Banach spaces for C1,ω,C1,+, C1,+ loc , and C1,+ B-smooth functions

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On Whitney-type extension theorems on Banach spaces for C1,ω,C1,+, C1,+ loc , and C1,+ B-smooth functions

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On Whitney-type extension theorems on Banach spaces for C1,ω,C1,+, C1,+ loc , and C1,+ B-smooth functions

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

1096-0813

Svazek periodika

532

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

127976

Kód UT WoS článku

001125488400001

EID výsledku v databázi Scopus

2-s2.0-85177999921