Let
N
N
be a Lie group with its Lie algebra generated by the left-invariant vector fields
X
1
,
…
,
X
k
{X_1}, \ldots ,{X_k}
on
N
N
. An explicit fundamental solution for the (hypoelliptic) operator
L
=
X
1
2
+
⋯
+
X
k
2
L = X_1^2 + \cdots + X_k^2
on
N
N
has been obtained for the Heisenberg group by Folland [1] and for the nilpotent (Iwasawa) groups of isometries of rank-one symmetric spaces by Kaplan and Putz [2]. Recently Kaplan [3] introduced a (still larger) class of step-
2
2
nilpotent groups
N
N
arising from Clifford modules for which similar explicit solutions exist. As in the case of
L
L
being the ordinary Laplacian on
N
=
R
k
N = {{\mathbf {R}}^k}
, these solutions are of the form
g
↦
const
‖
g
‖
2
−
m
g \mapsto {\text {const}}{\left \| g \right \|^{2 - m}}
,
g
∈
N
g \in N
, where the "norm" function
‖
‖
\left \| {} \right \|
satisfies a certain homogeneity condition. We prove that the above norm is also subadditive.