Compact embeddings of Bessel-Potential-Type spaces into generalized Hölder spaces involving k-modulus of smoothness

0354220 - MÚ 2012 RIV DE eng J - Journal Article
Gogatishvili, Amiran - Neves, J. S. - Opic, B.
Compact embeddings of Bessel-Potential-Type spaces into generalized Hölder spaces involving k-modulus of smoothness.
Zeitschrift für Analysis und Ihre Anwendungen. Roč. 30, č. 1 (2011), s. 1-27. ISSN 0232-2064. E-ISSN 1661-4534
R&D Projects: GA ČR GA201/08/0383
Institutional research plan: CEZ:AV0Z10190503
Keywords : Bessel potentials * Sobolev-type spaces * rearrangement-invariant Banach function spaces
Subject RIV: BA - General Mathematics
Impact factor: 0.327, year: 2011
http://www.ems-ph.org/journals/show_abstract.php?issn=0232-2064&vol=30&iss=1&rank=1

We present conditions which are necessary and sufficient for compact embeddings of Bessel potential spaces H σ X(IRn ), modelled upon a rearrangement-invariant Banach function spaces X(IRn ), into generalized Hölder spaces involving k-modulus of smoothness. To this end, we derive a characterization of compact subsets of generalized Hölder spaces. We apply our results to the case when X(IRn ) is a Lorentz-Karamata space Lp,q;b(IRn ). Applications cover both superlimiting and limiting cases.
Permanent Link: http://hdl.handle.net/11104/0193271