Study Of Some Local Two-Weight Integral Inequalities

When 0 < α < 1, Ding Shusen and other authors have obtained some weighted integral inequalities, but when α = 1, weighted integral inequalities have not been studied generally. In this paper, we first introduce a new kind of Aλ3r (λ1, λ2,Ω) two-weight, then we obtain some two-weight integral inequalities which are generalizations of the imbedding theorems, Poincare inequality, Caccioppoli-type estimate and weak reverse Holder inequality for differential forms when α= 1. These inequalities are extensions of classical results and can be used to study the integrability of differential forms and to estimate the integrals of differential forms. Finally, we give some applications of the above results.