Estimates of s-numbers of a Sobolev embedding involving spaces of variable exponent

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F15%3A00242123" target="_blank" >RIV/68407700:21110/15:00242123 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jmaa.2015.05.043" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2015.05.043</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2015.05.043" target="_blank" >10.1016/j.jmaa.2015.05.043</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Estimates of s-numbers of a Sobolev embedding involving spaces of variable exponent

Popis výsledku v původním jazyce

Let Omega be a bounded open subset of R-d, suppose that p(center dot) : Omega -> (1, infinity) is a bounded, log-Holder continuous function, and let L-p(center dot) (Omega), W-p(center dot)(o1)(Omega) be the usual variable exponent Lebesgue space and thecorresponding Sobolev space. The natural embedding id : W-p(center dot)(o1)(Omega) -> L-p(center dot)(Omega) is compact; when Omega is a bounded domain it is shown that there are positive constants K-1, K-2 such that for all n is an element of N, K-1 <=n(1/d)s(n)(id) <= K-2, where s(n)(id) is the nth approximation, Bernstein, Gelfand or Kolmogorov number of id. When p is constant this result is familiar; for variable p and d > 1 it appears to be the first result available for s-numbers of Sobolev exnbeddings. The paper also contains a sharp estimate of the norm of embeddings between L-p(center dot)(Omega) spaces which is interesting in its own right. K-1 <= n(1/d)s(n)(id) <= K-2, where s(n)(id) is the nth approximation, Bernstein, Gel

Název v anglickém jazyce

Estimates of s-numbers of a Sobolev embedding involving spaces of variable exponent

Popis výsledku anglicky

Let Omega be a bounded open subset of R-d, suppose that p(center dot) : Omega -> (1, infinity) is a bounded, log-Holder continuous function, and let L-p(center dot) (Omega), W-p(center dot)(o1)(Omega) be the usual variable exponent Lebesgue space and thecorresponding Sobolev space. The natural embedding id : W-p(center dot)(o1)(Omega) -> L-p(center dot)(Omega) is compact; when Omega is a bounded domain it is shown that there are positive constants K-1, K-2 such that for all n is an element of N, K-1 <=n(1/d)s(n)(id) <= K-2, where s(n)(id) is the nth approximation, Bernstein, Gelfand or Kolmogorov number of id. When p is constant this result is familiar; for variable p and d > 1 it appears to be the first result available for s-numbers of Sobolev exnbeddings. The paper also contains a sharp estimate of the norm of embeddings between L-p(center dot)(Omega) spaces which is interesting in its own right. K-1 <= n(1/d)s(n)(id) <= K-2, where s(n)(id) is the nth approximation, Bernstein, Gel

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA13-14743S" target="_blank" >GA13-14743S: Prostory funkcí, váhové nerovnosti a interpolace II</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2015

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

—

Svazek periodika

430

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

1088-1101

Kód UT WoS článku

000356126300030

EID výsledku v databázi Scopus

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