Isomorphic properties of quasi-elliptic operators (Q1594303)

The author considers a class of quasi-elliptic matrix differential operators with constant coefficients in the whole space \(\mathbb{R}^n\). He introduces a special class of weighted Sobolev spaces \(W^r_{p,\sigma}(\mathbb{R}^n)\) and proves that these operators define an isomorphism between \(W^r_{p,1}\) and \(L_p\). The results here proposed extend some previous theorems of Cantor, Y. Choquet-Bruhat and the author.