Calderón–Zygmund theory on some Lie groups of exponential growth

Let G = N X A, where N is a stratified Lie group and A = R^+ acts on N via automorphic dilations. We prove that the group G has the Calderon-Zygmund property, in the sense of Hebisch and Steger, with respect to a family of flow measures and metrics. This generalizes in various directions previous works by Hebisch and Steger and Martini et al., and provides a new approach in the development of the Calderon-Zygmund theory in Lie groups of exponential growth. We also prove a weak-type (1,1) estimate for the Hardy-Littlewood maximal operator naturally arising in this setting.