Abstract
This chapter is meant to give a brief and by no means complete description of the Heisenberg group \(\mathbb {H}\), that will be the setting of this work. Customarily this group is presented as a particular group on \(\mathbb {R}^3\). This is not restrictive and to explain why we recall some definitions and basic properties of Carnot groups in order to make the exposition self-contained. We refer to the monograph (Bonfiglioli et al., Stratified Lie Groups and Potential Theory for their Sub-Laplacians, 2007 [1]) for a complete presentation of Carnot groups.
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Bonfiglioli, A., Lanconelli, E., Uguzzoni, F.: Stratified Lie Groups and Potential Theory for Their Sub-Laplacians. Springer Monographs in Mathematics. Springer, Berlin (2007)
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Ricciotti, D. (2015). The Heisenberg Group. In: p-Laplace Equation in the Heisenberg Group. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-23790-9_2
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DOI: https://doi.org/10.1007/978-3-319-23790-9_2
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