Calderón–Zygmund theory on some Lie groups of exponential growth

Let G=N⋊A$G = N \rtimes A$, where N$N$ is a stratified Lie group and A=R+$A= \mathbb {R}_+$ acts on N$N$ via automorphic dilations. We prove that the group G$G$ has the Calderón–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 Calderón–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.