Interpolation of gentle spaces (Q1725005)

Summary: 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 \(\gamma\)-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.