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arXiv · 2311.01824

Calder\'on-Zygmund theory on some Lie groups of exponential growth

Filippo De Mari·Matteo Levi·Matteo Monti·Maria Vallarino
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Abstract

Let $G = N \rtimes A$, where $N$ is a stratified Lie group and $A= \mathbb R_+$ acts on $N$ via automorphic dilations. We prove that the group $G$ has the Calder\'on-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, Ottazzi and Vallarino, and provides a new approach in the development of Calder\'on-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.

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Filippo De Mari, Matteo Levi, Matteo Monti, Maria Vallarino. 2023-11-03. Calder\'on-Zygmund theory on some Lie groups of exponential growth. https://arxiv.org/abs/2311.01824

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