Sharp estimates of the k-modulus of smoothness of Bessel potentials
Result 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
Keywords
The result's identifiers
Result code in IS VaVaI
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
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
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
GA201/08/0383: Function Spaces, Weighted Inequalities and Interpolation
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2010
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 the London Mathematical Society
ISSN
0024-6107
e-ISSN
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Volume of the periodical
81
Issue of the periodical within the volume
3
Country of publishing house
GB - UNITED KINGDOM
Number of pages
17
Pages from-to
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UT code for WoS article
000278819000006
EID of the result in the Scopus database
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Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2010