Characterizations of Orlicz-Sobolev Spaces by Means of Generalized Orlicz-Poincaré Inequalities
Let Φ be an N-function. We show that a function u∈LΦ(ℝn) belongs to the Orlicz-Sobolev space W1,Φ(ℝn) if and only if it satisfies the (generalized) Φ-Poincaré inequality. Under more restrictive assumptions on Φ, an analog of the result holds in a general metric measure space setting.
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/426067 |
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| _version_ | 1832567103733891072 |
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| author | Toni Heikkinen |
| author_facet | Toni Heikkinen |
| author_sort | Toni Heikkinen |
| collection | DOAJ |
| description | Let Φ be an N-function. We show that a function u∈LΦ(ℝn) belongs to the Orlicz-Sobolev space W1,Φ(ℝn) if and only if it satisfies the (generalized) Φ-Poincaré inequality. Under more restrictive assumptions on Φ, an analog of the result holds in a general metric measure space setting. |
| format | Article |
| id | doaj-art-6b7dd67420a4498e861fe0a2341c10dd |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-6b7dd67420a4498e861fe0a2341c10dd2025-02-03T01:02:18ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/426067426067Characterizations of Orlicz-Sobolev Spaces by Means of Generalized Orlicz-Poincaré InequalitiesToni Heikkinen0Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, 40014 Jyväskylä, FinlandLet Φ be an N-function. We show that a function u∈LΦ(ℝn) belongs to the Orlicz-Sobolev space W1,Φ(ℝn) if and only if it satisfies the (generalized) Φ-Poincaré inequality. Under more restrictive assumptions on Φ, an analog of the result holds in a general metric measure space setting.http://dx.doi.org/10.1155/2012/426067 |
| spellingShingle | Toni Heikkinen Characterizations of Orlicz-Sobolev Spaces by Means of Generalized Orlicz-Poincaré Inequalities Journal of Function Spaces and Applications |
| title | Characterizations of Orlicz-Sobolev Spaces by Means of Generalized Orlicz-Poincaré Inequalities |
| title_full | Characterizations of Orlicz-Sobolev Spaces by Means of Generalized Orlicz-Poincaré Inequalities |
| title_fullStr | Characterizations of Orlicz-Sobolev Spaces by Means of Generalized Orlicz-Poincaré Inequalities |
| title_full_unstemmed | Characterizations of Orlicz-Sobolev Spaces by Means of Generalized Orlicz-Poincaré Inequalities |
| title_short | Characterizations of Orlicz-Sobolev Spaces by Means of Generalized Orlicz-Poincaré Inequalities |
| title_sort | characterizations of orlicz sobolev spaces by means of generalized orlicz poincare inequalities |
| url | http://dx.doi.org/10.1155/2012/426067 |
| work_keys_str_mv | AT toniheikkinen characterizationsoforliczsobolevspacesbymeansofgeneralizedorliczpoincareinequalities |