论文标题
改善了咖啡雷利 - 科恩 - 尼伦贝格的不平等和不确定性原则
Improved Caffarelli-Kohn-Nirenberg Inequalities and Uncertainty Principle
论文作者
论文摘要
在本文中，我们证明了一些改进的Caffarelli-Kohn-Nirenberg的不平等和不确定性原理，用于$ \ Mathbb r^n $的复合物和矢量值函数，这是对\ cite {dang-dang-deng-qian}结果的进一步研究。特别是，我们引入了用于矢量值函数的“相衍生物”的类似物。此外，使用引入的“相衍生物”，我们将超强的不确定性原理扩展到$ \ Mathbb s^n，n \ geq的复合物和矢量值函数的情况。
In this paper we prove some improved Caffarelli-Kohn-Nirenberg inequalities and uncertainty principle for complex- and vector-valued functions on $\mathbb R^n$, which is a further study of the results in \cite{Dang-Deng-Qian}. In particular, we introduce an analogue of "phase derivative" for vector-valued functions. Moreover, using the introduced "phase derivative", we extend the extra-strong uncertainty principle to cases for complex- and vector-valued functions defined on $\mathbb S^n,n\geq 2.$
