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Embeddings of Sobolev-type spaces into generalized Hölder spaces involving k-modulus of smoothness
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SYSNO ASEP 0442892 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Embeddings of Sobolev-type spaces into generalized Hölder spaces involving k-modulus of smoothness Author(s) Gogatishvili, Amiran (MU-W) RID, ORCID, SAI
Moura, S. (PT)
Neves, J. S. (PT)
Opic, B. (CZ)Source Title Annali di Matematica Pura ed Applicata. - : Springer - ISSN 0373-3114
Roč. 194, č. 2 (2015), s. 425-450Number of pages 26 s. Language eng - English Country DE - Germany Keywords rearrangement-invariant Banach function space ; modulus of smoothness ; distributional gradient Subject RIV BA - General Mathematics R&D Projects GA13-14743S GA ČR - Czech Science Foundation (CSF) GA201/08/0383 GA ČR - Czech Science Foundation (CSF) Institutional support MU-W - RVO:67985840 UT WOS 000351388800007 EID SCOPUS 84958771212 DOI 10.1007/s10231-013-0383-1 Annotation We use an estimate of the k-modulus of smoothness of a function f such that the norm of its distributional gradient ... k f belongs locally to the Lorentz space Ln/k,1(Rn), k ... N, k ... n, and we prove its reverse form to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces. These spaces are modelled upon rearrangement-invariant Banach function spaces X(Rn). Target spaces of our embeddings are generalized Hölder spaces defined by means of the k-modulus of smoothness (k...N). General results are illustrated with examples. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2016
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