Weighted Poincaré Inequalities For Green Operator And Applications

It is necessary to generalize the classical inequalities to weighted forms. These generalizations are useful not only in theories, but also in applications.By using the generalized Holder inequality, a new and most general weight-Arλ3(λ1,λ2,Ω)-weight, and the technique of weighted functions, we give in this paper the weighted Poincare inequality for Green's operator. These results can be viewed as generalizations of the classical results.Some applications of these inequalities to weak solutions of A-harmonic equations and quasiregular mappings in high dimensional spaces are also given.