Douglis--Nirenberg elliptic systems in H\"ormander spaces

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 $+\mathrm{\infty }$, considered as a function of $(1+\mathrm{\mid }\xi {\mathrm{\mid }}^2{)}^{1\mathrm{/}2}$ 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.