Improved Caffarelli-Kohn-Nirenberg Inequalities and Uncertainty Principle

被引：1
|
作者：
Dang, Pei [1 ]
Mai, Weixiong [2 ]
机构：
[1] Macau Univ Sci & Technol, Fac Innovat Engn, Dept Engn Sci, Macau, Peoples R China
[2] Macau Univ Sci & Technol, Macao Ctr Math Sci, Macau, Peoples R China
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2024年 / 34卷 / 03期
关键词：
Uncertainty principles; Caffarelli-Kohn-Nirenberg inequalities; Phase derivative; Covariance; RELLICH; SIGNALS; HARDY; MANIFOLDS; SOBOLEV;
D O I：
10.1007/s12220-023-01524-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we prove some improved Caffarelli-Kohn-Nirenberg inequalities and uncertainty principle for complex- and vector-valued functions on R-n, which is a further study of the results in Dang et al. (J Funct Anal 265:2239-2266, 2013). 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 S-n, n >= 2.
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