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Douglis--Nirenberg elliptic systems in Hörmander spaces

We investigate Douglis--Nirenberg uniformly elliptic systems in $\mathbb{R}^{n}$ on a class of Hörmander inner product spaces. They are parametrized with a radial function parameter which is RO-varying at $+\infty$, considered as a function of $(1+|ξ|^{2})^{1/2}$ with $ξ\in\mathbb{R}^{n}$. 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.