Optimal Constants of Smoothing Estimates for the 2D Dirac Equation

In this paper, we discuss optimal constants and extremisers of Kato-smoothing estimates for the 2D Dirac equation. Smoothing estimates are inequalities that express the smoothing effect of dispersive equations, and detailed information regarding optimal constants and extremisers for wide classes of...

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Bibliographic Details
Published in:The Journal of fourier analysis and applications 2022-08, Vol.28 (4), Article 57
Main Author: Ikoma, Makoto
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Approximations and Expansions
Constants
Dirac equation
Estimates
Fourier Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Partial Differential Equations
Signal,Image and Speech Processing
Smoothing
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Summary:In this paper, we discuss optimal constants and extremisers of Kato-smoothing estimates for the 2D Dirac equation. Smoothing estimates are inequalities that express the smoothing effect of dispersive equations, and detailed information regarding optimal constants and extremisers for wide classes of Kato-smoothing estimates were given in the last several year by Bez et al. (Adv Math 285:1767–1795, 2015) and Bez and Sugimoto (J Anal Math 131:159–187, 2017). This paper is a trial to generalize these previous results to include the Dirac equation which is outside the framework of them.
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-022-09950-6