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

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Type: Preprint
National /International: International
Title: Characterization of embeddings of Sobolev-type spaces into generalized Hölder spaces defined by Lp-modulus of smoothness
Publication Date: 2018-04-20
Authors: - Amiran Gogatishvili
- Júlio Severino das Neves
- Bohumír Opic
Abstract: We prove a sharp estimate for the k-modulus of smoothness, modelled upon a p-Lebesgue space, of a function f in WkL pn/(n+kp),p(Ω) + Wk Lp(Ω), where Ω is a domain with minimally smooth boundary and finite Lebesgue measure. 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.
Institution: DMUC 18-14
Online version: http://www.mat.uc.pt...prints/eng_2018.html
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