Littlewood–Paley decompositions and Besov spaces on Lie groups of polynomial growth

We introduce a Littlewood–Paley decomposition related to any sub‐Laplacian on a Lie group G of polynomial volume growth; this allows us to prove a Littlewood–Paley theorem in this general setting and to provide a dyadic characterization of Besov spaces B s,q p ( G ), s ∈ ℝ, equivalent to the classical definition through the heat kernel. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)