中文摘要：

本研究把标量函数的Adams不等式推广到向量值函数的情形,证明了当n=2k时,采用两种等价的范数,向量值函数的Adams不等式都是成立的,并且这2个不等式的上确界是相等的。该向量值函数的Adams不等式,可以应用到物理和几何中常出现的方程组,而传统的Adams不等式不具备这样的能力。

英文摘要：

In this paper,we generalize the Adams inequality of the case of scalar functions to the case of vector functions. When n =2k,we prove that the Adams inequalities under two equivalent Sobolev norms are both true. Moreover,the two supremums of the inequalities are equal to each other. This kind of vector valued inequality can be used in some systems of partial differential equations arising out of geometric and physical problems to which are not suitable to apply the inequality for scalar functions.