中文摘要：

将经典的关于函数的Sobolev嵌入定理推广到微分形式空间。结合已有的函数方面的结论以及微分形式自身的性质，利用Minkowski不等式等基本不等式，建立微分形式Sobolev空间W1,P（Ω，∧）的嵌入定理；根据函数形式的Sobolev紧嵌入定理的结果，主要借助于对角线法则，证得微分形式空间W1，P（Ω，∧l）的紧嵌入定理；并将上述结论推广到一般的微分形式Sob01ev空间矿，一（Ω，∧l）。

英文摘要：

The classical Sobolev imbedding theorem is generalized to Sobolev spaces of differential forms. Firstly, together with the results in terms of functions and properties of differential forms themselves, the imbedding theorem for Sobolev spaces W1,P（Ω,∧l） is established by Minkowski inequality and other fundamental inequalities. Second- ly, applying the compact imbedding results in terms of functions, the compact imbedding theorem of W1,P（Ω,∧l） is obtained by the diagonal rule. Lastly, the above results are extended to more general spaces W1,P（Ω,∧l）.