Weighted Caffarelli-Kohn-Nirenberg type inequality on the Heisenberg group
Weighted Caffarelli-Kohn-Nirenberg type inequality on the Heisenberg group
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DOI：
10.1007/s13226-015-0118-7
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发表时间：
2015-04
影响因子：
0.7
通讯作者：
Yazhou Han
中科院分区：
文献类型：
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作者：
Yazhou Han
建立了Heisenberg群上的一类Caffarelli-Kohn-Nirenberg型不等式.受Chern和Lin思想的启发，引入了一个函数变换。结合一些初等不等式和精确估计，建立了一类加权Hardy-Sobolev型不等式，并得到了我们的主要结果，即Heisenberg群上的Caffarelli-Kohn-Nirenberg型不等式.
This work is devoted to establish a class of Caffarelli-Kohn-Nirenberg type inequalities on the Heisenberg group. Inspired by the idea of Chern and Lin, a function transformation is introduced. Combining some elementary inequalities and some accurate estimates, we establish a class of weighted Hardy-Sobolev type inequalities and then obtain our main result, namely Caffarelli-Kohn-Nirenberg type inequalities on the Heisenberg group.