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.

引用

页数：26

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