  We say that a tempered distribution $A$ belongs to the class $S^m(\Ge)$ on a
homogeneous Lie algebra $\Ge$ if its Abelian Fourier transform $a=\hat{A}$ is a
smooth function on the dual $\Ges$ and satisfies the estimates $$
|D^{\alpha}a(\xi)|\le C_{\alpha}(1+|\xi|)^{m-|\alpha|}. $$ Let $A\in S^0(\Ge)$.
Then the operator $f\mapsto f\star\widetilde{A}(x)$ is bounded on $L^2(\Ge)$.
Suppose that the operator is invertible and denote by $B$ the convolution
kernel of its inverse. We show that $B$ belongs to the class $S^0(\Ge)$ as
well. As a corollary we generalize Melin's theorem on the parametrix
construction for Rockland operators.
