Characterization of embeddings of Sobolev-type spaces into generalized Hölder spaces defined by Lp-modulus of smoothness |
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Authors: | Amiran Gogatishvili Júlio S Neves Bohumír Opic |
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Institution: | 1. Institute of Mathematics, Academy of Sciences of the Czech Republic, Z?itná 25, 11567 Prague 1, Czech Republic;2. CMUC, Department of Mathematics, University of Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal;3. Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic |
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Abstract: | We prove a sharp estimate for the k-modulus of smoothness, modelled upon a -Lebesgue space, of a function f in , where Ω is a domain with minimally smooth boundary and finite Lebesgue measure, , and . 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. |
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Keywords: | 26D15 26B35 26A15 26A16 46E30 46E35 46B42 Rearrangement-invariant Banach function spaces Sobolev-type and Hölder-type spaces Hardy-type operators Embeddings |
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