Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddings
Let Dkf mean the vector composed by all partial derivatives of order k of a function f(x), x∈Ω⊂ℝn. Given a Banach function space A, we look for a possibly small space B such that ‖f‖B≤c‖|Dkf|‖A for all f∈C0k(Ω). The estimates obtained are applied to ultrasymmetric spaces A=Lφ,E, B=Lψ,E, giving some...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2005/254184 |
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| _version_ | 1849307596002951168 |
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| author | Evgeniy Pustylnik |
| author_facet | Evgeniy Pustylnik |
| author_sort | Evgeniy Pustylnik |
| collection | DOAJ |
| description | Let Dkf mean the vector composed by all partial derivatives of order k of a function f(x), x∈Ω⊂ℝn. Given a Banach function space A, we look for a possibly small space B such that ‖f‖B≤c‖|Dkf|‖A for all f∈C0k(Ω). The estimates obtained are applied to ultrasymmetric spaces A=Lφ,E, B=Lψ,E, giving some optimal (or rather sharp) relations between parameter-functions φ(t) and ψ(t) and new results for embeddings of Orlicz-Sobolev spaces. |
| format | Article |
| id | doaj-art-28075a429d5c4ebc8dfc1f4a0500a22c |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-28075a429d5c4ebc8dfc1f4a0500a22c2025-08-20T03:54:42ZengWileyJournal of Function Spaces and Applications0972-68022005-01-013218320810.1155/2005/254184Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddingsEvgeniy Pustylnik0Department of Mathematics, Technion—Israel Institute of Technology, Haifa 32000, IsraelLet Dkf mean the vector composed by all partial derivatives of order k of a function f(x), x∈Ω⊂ℝn. Given a Banach function space A, we look for a possibly small space B such that ‖f‖B≤c‖|Dkf|‖A for all f∈C0k(Ω). The estimates obtained are applied to ultrasymmetric spaces A=Lφ,E, B=Lψ,E, giving some optimal (or rather sharp) relations between parameter-functions φ(t) and ψ(t) and new results for embeddings of Orlicz-Sobolev spaces.http://dx.doi.org/10.1155/2005/254184 |
| spellingShingle | Evgeniy Pustylnik Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddings Journal of Function Spaces and Applications |
| title | Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddings |
| title_full | Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddings |
| title_fullStr | Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddings |
| title_full_unstemmed | Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddings |
| title_short | Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddings |
| title_sort | sobolev type inequalities in ultrasymmetric spaces with applications to orlicz sobolev embeddings |
| url | http://dx.doi.org/10.1155/2005/254184 |
| work_keys_str_mv | AT evgeniypustylnik sobolevtypeinequalitiesinultrasymmetricspaceswithapplicationstoorliczsobolevembeddings |