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

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Let X(n)=X(n, µn) be a rearrangement-invariant Banach function space over the measure space (n, µn), where µn 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 function fX(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. Let X(n)=X(n, µn) be a rearrangement-invariant Banach function space over the measure space (n, µn), where µn 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 function fX(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. (en)
Title	Sharp estimates of the k-modulus of smoothness of Bessel potentials Sharp estimates of the k-modulus of smoothness of Bessel potentials (en)
skos:prefLabel	Sharp estimates of the k-modulus of smoothness of Bessel potentials Sharp estimates of the k-modulus of smoothness of Bessel potentials (en)
skos:notation	RIV/67985840:_____/10:00342833!RIV11-GA0-67985840
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/08/0383), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Gogatishvili, Amiran Opic, Bohumír
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	287174
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/10:00342833
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	embeddings; spaces; optimality; compact (en)
http://linked.open.../riv/klicoveSlovo	spaces compact embeddings optimality
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[8522F03352ED]
http://linked.open...i/riv/nazevZdroje	Journal of the London Mathematical Society
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Function Spaces, Weighted Inequalities and Interpolation
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	81
http://linked.open...iv/tvurceVysledku	Gogatishvili, Amiran Neves, J. S. Opic, Bohumír
http://linked.open...ain/vavai/riv/wos	000278819000006
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi
issn	0024-6107
number of pages	17 (xsd:int)

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