Fredholm property of regular hypoelliptic operators on the scales of multianisotropic spaces

Abstract

This paper studies the Fredholm properties for a class of regular hypoelliptic operators. We establish necessary and sufficient conditions for a priori estimates for differential operators acting in multianisotropic Sobolev spaces in Rn. Fredholm criteria and index invariance are obtained for a wide class of regular hypoelliptic operators on the special scales of multianisotropic weighted spaces.