Počet záznamů: 1

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

  1. 1.
    0342833 - MU-W 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
    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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