For a smooth oriented Riemannian -manifold without boundary, let and be two closed differential forms, where satisfy Sobolev’s relation . The pair is called admissible pair if and , where .
In this paper, the authors prove that, for almost every ball in , an admissible pair satisfies
where and . As applications they obtain an isoperimetric type inequality and the Hölder continuity property for solutions of Hodge systems.