Douglis--Nirenberg elliptic systems in Hörmander spaces

Abstract

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 $(1+|\xi {|}^2{)}^{1/2}$ 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.

14 pages, in Russian