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Abstract and Applied Analysis
Volume 2014, Article ID 801531, 9 pages
http://dx.doi.org/10.1155/2014/801531
Research Article

Interpolation of Gentle Spaces

1Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2Université de Tunis El Manar, Faculté des Sciences de Tunis, Laboratoire de Recherche Équations aux Dérivées Partielles et Applications, 2092 Tunis, Tunisia

Received 1 November 2013; Revised 21 February 2014; Accepted 28 February 2014; Published 6 May 2014

Academic Editor: Paul W. Eloe

Copyright © 2014 Mourad Ben Slimane and Hnia Ben Braiek. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 and spaces are gentle. Further, an application to nonlinear approximation is presented.