New weighted integral inequalities for differential forms in some domains. (Q1587535)

In the first part of this paper the author proves some versions of the local weighted Poincaré type inequality for differential forms (Theorems 2.6, 2.14 and 2.21). Next, as applications of the obtained local results, the author proves global weighted integral inequalities for differential forms in \(L^s(\mu)-\)averaging domains (Theorem 3.1) and in John domains (Theorem 3.8). These results can be considered as generalizations of the classical Poincaré-type inequality.