Improved Caffarelli-Kohn-Nirenberg Inequalities and Uncertainty Principle

Pei Dang, Weixiong Mai

Published 2022-10-07Version 1

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}. Moreover, we also extend the extra-strong uncertainty principle given in \cite{Dang-Qian-Chen} to cases for complex- and vector-valued functions defined on $\mathbb S^n,n\geq 2.$