Interpolation of Gentle Spaces
The notion of gentle spaces, introduced by Jaffard, describes what would be an “ideal” function space to work with wavelet coefficients. It is based mainly on the separability, the existence of bases, the homogeneity, and the γ-stability. We prove that real and complex interpolation spaces between t...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/801531 |
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| _version_ | 1832560889814843392 |
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| author | Mourad Ben Slimane Hnia Ben Braiek |
| author_facet | Mourad Ben Slimane Hnia Ben Braiek |
| author_sort | Mourad Ben Slimane |
| collection | DOAJ |
| description | The notion of gentle spaces, introduced by Jaffard, describes what would be an “ideal” function space to work with wavelet coefficients. It is based mainly on the separability, the existence of bases, the homogeneity, and the γ-stability. We prove that real and complex interpolation spaces between two gentle spaces are also gentle. This shows the relevance and the stability of this notion. We deduce that Lorentz spaces Lp,q and Hp,q spaces are gentle. Further, an application to nonlinear approximation is presented. |
| format | Article |
| id | doaj-art-ab15f9e623894a89ac01c4478d791fb3 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ab15f9e623894a89ac01c4478d791fb32025-02-03T01:26:28ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/801531801531Interpolation of Gentle SpacesMourad Ben Slimane0Hnia Ben Braiek1Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaUniversité de Tunis El Manar, Faculté des Sciences de Tunis, Laboratoire de Recherche Équations aux Dérivées Partielles et Applications, 2092 Tunis, TunisiaThe notion of gentle spaces, introduced by Jaffard, describes what would be an “ideal” function space to work with wavelet coefficients. It is based mainly on the separability, the existence of bases, the homogeneity, and the γ-stability. We prove that real and complex interpolation spaces between two gentle spaces are also gentle. This shows the relevance and the stability of this notion. We deduce that Lorentz spaces Lp,q and Hp,q spaces are gentle. Further, an application to nonlinear approximation is presented.http://dx.doi.org/10.1155/2014/801531 |
| spellingShingle | Mourad Ben Slimane Hnia Ben Braiek Interpolation of Gentle Spaces Abstract and Applied Analysis |
| title | Interpolation of Gentle Spaces |
| title_full | Interpolation of Gentle Spaces |
| title_fullStr | Interpolation of Gentle Spaces |
| title_full_unstemmed | Interpolation of Gentle Spaces |
| title_short | Interpolation of Gentle Spaces |
| title_sort | interpolation of gentle spaces |
| url | http://dx.doi.org/10.1155/2014/801531 |
| work_keys_str_mv | AT mouradbenslimane interpolationofgentlespaces AT hniabenbraiek interpolationofgentlespaces |