## Abstract and Applied Analysis

### Interpolation of Gentle Spaces

#### 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 ${L}^{p,q}$ and ${H}^{p,q}$ spaces are gentle. Further, an application to nonlinear approximation is presented.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 801531, 9 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412276968

Digital Object Identifier
doi:10.1155/2014/801531

Mathematical Reviews number (MathSciNet)
MR3208568

Zentralblatt MATH identifier
1261.46020

#### Citation

Ben Slimane, Mourad; Ben Braiek, Hnia. Interpolation of Gentle Spaces. Abstr. Appl. Anal. 2014 (2014), Article ID 801531, 9 pages. doi:10.1155/2014/801531. https://projecteuclid.org/euclid.aaa/1412276968

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