Littlewood-Paley characterization of Hölder-Zygmund spaces on stratified Lie groups

summary:We give a characterization of the Hölder-Zygmund spaces $\mathcal {C}^{\sigma }(G)$ ($0< \sigma <\infty $) on a stratified Lie group $G$ in terms of Littlewood-Paley type decompositions, in analogy to the well-known characterization of the Euclidean case. Such decompositions are defined via the spectral measure of a sub-Laplacian on $G$, in place of the Fourier transform in the classical setting. Our approach mainly relies on almost orthogonality estimates and can be used to study other function spaces such as Besov and Triebel-Lizorkin spaces on stratified Lie groups