Improved Caffarelli–Kohn–Nirenberg Inequalities and Uncertainty Principle

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 derivat...

Full description

Saved in:
Bibliographic Details
Published inThe Journal of geometric analysis Vol. 34; no. 3
Main Authors Dang, Pei, Mai, Weixiong
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2024
Springer Nature B.V
Subjects
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Global Analysis and Analysis on Manifolds
Inequalities
Mathematics
Mathematics and Statistics
Principles
Uncertainty principles
Caffarelli–Kohn–Nirenberg inequalities
Uncertainty principles
Phase derivative
Covariance
Online AccessGet full text

Cover

More Information
Summary: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 .
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-023-01524-2