Carnot群上Stein-Weiss不等式最优解的存在性
Existence of optimizers of the Stein-Weiss inequalities on Carnot groups
摘要：
在一定条件下证明了Carnot群上Stein-Weiss不等式的最优解的存在性。Lions的集中紧性原理在卡诺群中的应用在我们的证明中起着重要的作用。与已知的海森堡群上Hardy-Littlewood-Sobolev不等式的处理不同，我们的讨论涉及到权函数的幂.
英文摘要：
This paper proves existence of optimizers of the Stein-Weiss inequalities on Carnot groups under some conditions. The adjustment of Lions' concentration compactness principles to Carnot groups plays an important role in our proof. Unlike known treatment to the Hardy-Littlewood-Sobolev inequality on Heisenberg group, our arguments relate to the powers of the weight functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
