Polar coordinates in Carnot groups

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Best constants for Moser-Trudinger inequalities on the Heisenberg group (2001, methodology): “Their constant can be calculated explicitly for the Heisenberg group and groups of Heisenberg type and coincides with the constants obtained in this paper and also [CoL] (see also a calculation of the constant on the H-type groups in [ BT ]).”
Boundary Harnack Principle for p-harmonic Functions in Smooth Euclidean Domains (2007, methodology): “It is worth noting that the results and techniques discussed in this paper are valid for other metric measure spaces such as the Heisenberg groups and polarizable Carnot groups (see [7] for more on polarizable Carnot groups), provided we concentrate on domains that satisfy the ball condition.”
Hardy-type inequalities related to degenerate elliptic differential operators (2006, background): “Moreover, with analogous computations of [2], it is possible to show that there exists a constant l p = 0 such that −L p p = l pδ0 on RN (3.”