论文标题
关于（非）径向Sobolev空间的紧凑性
On the compactness of the (non)radial Sobolev spaces
论文作者
论文摘要
在本说明中，我们在[18]中给出了问题的肯定答案，这是非sobolev空间的紧凑性结果。作为应用程序，我们显示了在球形平均零下的关键硬性不平等的极端功能。接下来，我们改善了[8]中径向Sobolev空间的紧凑性结果。在附录中，我们在球形平均值零下提供了耐力类型不平等的替代证明。
In this note, we give the affirmative answer of the question in [18], which is a compactness result of the non-radial Sobolev spaces. As an application, we show the existence of an extremal function of the critical Hardy inequality under spherical average zero. Next, we give an improvement of the compactness results of the radial Sobolev spaces in [8]. In Appendix, we give an alternative proof of Hardy type inequalities under spherical average zero.
