Characterization of embeddings of Sobolev-type spaces into generalized Hölder spaces defined by Lp-modulus of smoothness

0497233 - MÚ 2020 RIV US eng J - Článek v odborném periodiku
Gogatishvili, Amiran - Neves, J. S. - Opic, B.
Characterization of embeddings of Sobolev-type spaces into generalized Hölder spaces defined by Lp-modulus of smoothness.
Journal of Functional Analysis. Roč. 276, č. 2 (2019), s. 636-657. ISSN 0022-1236. E-ISSN 1096-0783
Grant CEP: GA ČR(CZ) GA18-00580S
Institucionální podpora: RVO:67985840
Klíčová slova: rearrangement-invariant Banach function spaces * Sobolev-type and Hölder-type spaces * Hardy-type operators * embeddings
Obor OECD: Pure mathematics
Impakt faktor: 1.496, rok: 2019
Způsob publikování: Omezený přístup
http://dx.doi.org/10.1016/j.jfa.2018.10.023

We prove a sharp estimate for the k-modulus of smoothness, modelled upon a Lp-Lebesgue space, of a function f in WkL[Formula presented],p(Ω), where Ω is a domain with minimally smooth boundary and finite Lebesgue measure, k,n∈N, k<n and [Formula presented]<p<+∞. This sharp estimate is used to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces into generalized Hölder spaces defined by means of the k-modulus of smoothness. General results are illustrated with examples. In particular, we obtain a generalization of the classical Jawerth embeddings.
Trvalý link: http://hdl.handle.net/11104/0289809