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Sharp estimates of the k-modulus of smoothness of Bessel potentials
- 1.0342833 - MÚ 2011 RIV GB eng J - Článek v odborném periodiku
Gogatishvili, Amiran - Neves, J. S. - Opic, Bohumír
Sharp estimates of the k-modulus of smoothness of Bessel potentials.
Journal of the London Mathematical Society. Roč. 81, č. 3 (2010), s. 608-624. ISSN 0024-6107. E-ISSN 1469-7750
Grant CEP: GA ČR GA201/08/0383
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: embeddings * spaces * optimality * compact
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.828, rok: 2010
http://jlms.oxfordjournals.org/content/81/3/608
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.
Trvalý link: http://hdl.handle.net/11104/0185456
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