Sharp estimates of the k-modulus of smoothness of Bessel potentials

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F10%3A00342833" target="_blank" >RIV/67985840:_____/10:00342833 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Sharp estimates of the k-modulus of smoothness of Bessel potentials
Original language description
Let X(n)=X(n, ?n) be a rearrangement-invariant Banach function space over the measure space (n, ?n), where ?n stands for the n-dimensional Lebesgue measure in n. We derive a sharp estimate for the k-modulus of smoothness of the convolution of a functionfX(n) with the Bessel potential kernel g, where (0, n). The above estimate is very important in applications. For example, it enables us to derive optimal continuous embeddings of Bessel potential spaces HX(n) in a forthcoming paper, where, in limiting situations, we are able to obtain embeddings into Zygmund-type spaces rather than Hölder-type spaces. In particular, such results show that the Brézis?Wainger embedding of the Sobolev space Wk+1, n/k(n), with k and k<n?1, into the space of almost? Lipschitz functions, is a consequence of a better embedding which has as its target a Zygmund-type space.
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/GA201%2F08%2F0383" target="_blank" >GA201/08/0383: Function Spaces, Weighted Inequalities and Interpolation</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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