Embeddings of Sobolev-type spaces into generalized Hölder spaces involving k-modulus of smoothness

0442892 - MÚ 2016 RIV DE eng J - Journal Article
Gogatishvili, Amiran - Moura, S. - Neves, J. S. - Opic, B.
Embeddings of Sobolev-type spaces into generalized Hölder spaces involving k-modulus of smoothness.
Annali di Matematica Pura ed Applicata. Roč. 194, č. 2 (2015), s. 425-450. ISSN 0373-3114. E-ISSN 1618-1891
R&D Projects: GA ČR GA13-14743S; GA ČR GA201/08/0383
Institutional support: RVO:67985840
Keywords : rearrangement-invariant Banach function space * modulus of smoothness * distributional gradient
Subject RIV: BA - General Mathematics
Impact factor: 0.861, year: 2015
http://link.springer.com/article/10.1007/s10231-013-0383-1

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.
Permanent Link: http://hdl.handle.net/11104/0245695