Embeddings of Sobolev-type spaces into generalized Hölder spaces involving $$k$$ k -modulus of smoothness
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| 024 | 7 | 0 | |a 10.1007/s10231-013-0383-1 |2 doi |
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| 245 | 0 | 0 | |a Embeddings of Sobolev-type spaces into generalized Hölder spaces involving $$k$$ k -modulus of smoothness |h [Elektronische Daten] |c [Amiran Gogatishvili, Susana Moura, Júlio Neves, Bohumír Opic] |
| 520 | 3 | |a We use an estimate of the $$k$$ k -modulus of smoothness of a function $$f$$ f such that the norm of its distributional gradient $$|\nabla ^kf|$$ | ∇ k f | belongs locally to the Lorentz space $$L^{n/k, 1}({\mathbb {R}}^n),\,k \in {\mathbb {N}},\,k\le n$$ L n / k , 1 ( R n ) , 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 $$X({\mathbb {R}}^n)$$ X ( R n ) . Target spaces of our embeddings are generalized Hölder spaces defined by means of the $$k$$ k -modulus of smoothness $$(k\in {\mathbb {N}})$$ ( k ∈ N ) . General results are illustrated with examples. | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2013 | ||
| 690 | 7 | |a Rearrangement-invariant Banach function space |2 nationallicence | |
| 690 | 7 | |a Modulus of smoothness |2 nationallicence | |
| 690 | 7 | |a Distributional gradient |2 nationallicence | |
| 690 | 7 | |a Lorentz space |2 nationallicence | |
| 690 | 7 | |a Sobolev-type space |2 nationallicence | |
| 690 | 7 | |a Banach lattice |2 nationallicence | |
| 690 | 7 | |a Hölder-type space |2 nationallicence | |
| 690 | 7 | |a Embeddings |2 nationallicence | |
| 700 | 1 | |a Gogatishvili |D Amiran |u Institute of Mathematics, Academy of Sciences of the Czech Republic, Z̆ itná 25, 11567, Prague 1, Czech Republic |4 aut | |
| 700 | 1 | |a Moura |D Susana |u Department of Mathematics, CMUC, University of Coimbra, Apartado 3008, 3001-454, Coimbra, Portugal |4 aut | |
| 700 | 1 | |a Neves |D Júlio |u Department of Mathematics, CMUC, University of Coimbra, Apartado 3008, 3001-454, Coimbra, Portugal |4 aut | |
| 700 | 1 | |a Opic |D Bohumír |u Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675, Prague 8, Czech Republic |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/2(2015-04-01), 425-450 |x 0373-3114 |q 194:2<425 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-013-0383-1 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-013-0383-1 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Gogatishvili |D Amiran |u Institute of Mathematics, Academy of Sciences of the Czech Republic, Z̆ itná 25, 11567, Prague 1, Czech Republic |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Moura |D Susana |u Department of Mathematics, CMUC, University of Coimbra, Apartado 3008, 3001-454, Coimbra, Portugal |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Neves |D Júlio |u Department of Mathematics, CMUC, University of Coimbra, Apartado 3008, 3001-454, Coimbra, Portugal |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Opic |D Bohumír |u Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675, Prague 8, Czech Republic |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/2(2015-04-01), 425-450 |x 0373-3114 |q 194:2<425 |1 2015 |2 194 |o 10231 | ||