Weighted integral inequalities for differential forms (Q816449)

The aim of the paper is to derive two-weight integral inequalities involving differential forms. The authors called them the \(A_r(\lambda,\Omega)\)-weighted Poincaré inequality, the \(A_{r,\lambda}(\Omega)\)-weighted Caccioppoli inequality and the weighted weak reverse Hölder inequality. These results generalize those of \textit{C.\,A.\,Nolder} [Ill. J. Math. 43, 613--632 (1999; Zbl 0957.35046)] and can be used to study the integrability of differential forms and to estimate integrals of differential forms. As application of main theorems, three examples are given.