  We investigate Douglis--Nirenberg uniformly elliptic systems in
$\mathbb{R}^{n}$ on a class of H\"ormander inner product spaces. They are
parametrized with a radial function parameter which is RO-varying at $+\infty$,
considered as a function of $(1+|\xi|^{2})^{1/2}$ with $\xi\in\mathbb{R}^{n}$.
An a'priori estimate for solutions is proved, and their interior regularity is
studied. A sufficient condition for the systems to have the Fredholm property
is given.
