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.