Douglis-Nirenberg elliptic systems in Hörmander spaces

Abstract

We investigate Douglis-Nirenberg uniformly elliptic systems in $\mathbb{R}^n$ on the class of Hormander Hilbert spaces $H^{\varphi}$, where $\varphi$ is an $RO$-varying function of scalar argument. An a priori estimate for solutions is proved, and their interior regularity is studied. A sufficient condition for these systems to have the Fredholm property is given.