中文摘要：

微分形式是函数的自然推广,即函数为微分形式的0-形式,目前已成为许多数学分支（如微分几何）研究中的重要工具。本文证明了关于微分形式的Ar^λ1/λ2（λ1 λ2,; E）-权Caccioppoli-型Lp-不等式,此不等式可视为许多Caccioppoli-型加权不等式的推广,并给出了相应的Caccioppoli-型Lφ-不等式。

英文摘要：

Differential form is the natural generalization of the function, which is the differential form with 0- form. Furthermore, it has become an important tool in the study of many branches of mathematics, such as differential geometry. Firstly, we prove the Arλ1/λ2（λ1,λ2;E）- weighted Caccioppoli-type inequality with Lp - integration. It also can be seen as the generalization of many existing weighted Caccioppoli-type inequalities. Furthermore, we give the corresponding Caccioppoli-type inequality with Lφ - integration.