论文标题
caffarelli-kohn-nirenberg径向功能的不平等现象
The Caffarelli-Kohn-Nirenberg Inequalities For Radial Functions
论文作者
论文摘要
我们为Sobolev中的radial功能和订单的分数Sobolev空间$ 0 <s \ le 1 $建立了Caffarelli-Kohn-Nirenberg的全部范围。特别是，我们表明，径向函数的参数的范围严格比没有对称假设的参数大。以前的已知结果仅显示了一些特殊的参数范围，即使在此情况下$ s = 1 $。我们的证明是新的，可以很容易地适应其他情况。还提到了紧凑型嵌入的应用。
We establish the full range of the Caffarelli-Kohn-Nirenberg inequalities for radial functions in the Sobolev and the fractional Sobolev spaces of order $0 < s \le 1$. In particular, we show that the range of the parameters for radial functions is strictly larger than the one without symmetric assumption. Previous known results reveal only some special ranges of parameters even in the case $s=1$. Our proof is new and can be easily adapted to other contexts. Applications on compact embeddings are also mentioned.
