Quelques caractérisations des espaces de Hölder-Zygmund généralisés Λ_{σ,N}^{α}(R^d)

Generalized Hölder-Zygmund spaces $\Lambda_{\sigma, N}^{\alpha}(\R^{d})$ were recently introduced and are based on a generalization of Besov spaces. Under some conditions, generalized Hölder-Zygmund and Besov spaces are equal. It has been proved that most properties of classical Hölder-Zygmund spaces are held for spaces $\Lambda^{\sigma,\alpha}(\R^{d})$, which constitute a particular case of spaces $\Lambda_{\sigma, N}^{\alpha}(\R^{d})$ with $N_{j}=2^{j}$. The goal of the present document is to prove that most of these properties are kept for $\Lambda_{\sigma, N}^{\alpha}(\R^{d})$ spaces.Version en attente de soumission 02/201