A-harmonic Forms On Riemannian Manifolds

In this paper, we first give the definition for Ar(λ1,λ2, Q)-weight. This kind of weight is a generalization of the classical ones. Then we derive Ar(λi, A2,Ω)-weighted Sobolev-Poincare imbedding inequalities and Poincare inequalities for the composition of the Laplace-Beltrami operator, homotopy operator and Green's operator on Riemannian manifolds. These results can be used to study the integrability of A-harmonic forms and the properties of the related operators which are applied to A-harmonic forms on manifolds.