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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Estimates of s-numbers of a Sobolev embedding involving spaces of variable exponent
Original language description
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
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA13-14743S" target="_blank" >GA13-14743S: Function spaces, weighted inequalities and interpolation II</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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