Geodesic
A simple observation on Heisenberg-like uncertainty principles
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 49, Tome 503 (2021), pp. 113-120 
Yiyu Tang. A simple observation on Heisenberg-like uncertainty principles. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 49, Tome 503 (2021), pp. 113-120. http://geodesic.mathdoc.fr/item/ZNSL_2021_503_a6/
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     title = {A simple observation on {Heisenberg-like} uncertainty principles},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_503_a6/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A solution is given to a conjecture proposed recently by Y. Wigderson and A. Wigderson concerning a “Heisenberg-like” uncertainty principle. That conjecture is about the image of the map $ f \mapsto \frac{\|f\|_q\|\hat{f}\|_q}{\|f\|_2\|\hat{f}\|_2}, f\in \mathscr{S}(\mathbb{R})\setminus\{0\} $, where $\mathscr{S}(\mathbb{R}) $ stands for the Schwartz class of functions on the real line. Also, a more general question is answered, where the $L_2$ norm is replaced by the $L_p$ norm in the denominator.

[1] W. Bechner, “Inequalities in Fourier analysis”, Ann. Math., 102 (1975), 159–182 | DOI | MR

[2] L. Grafakos, Classical Fourier Analysis, Graduate Texts in Mathematics, 249, 3rd edition, Springer, 2014 | Zbl

[3] L. Huang, Z. Liu, J. Wu, Quantum smooth uncertainty principles for von Neumann bi-algebras, July 19, 2021, arXiv: 2107.09057

[4] Y. Tang (June 17–18, 2021), 2021 https://sites.google.com/view/oudynamicalsystems/complane

[5] Y. Wigderson, A. Wigderson, “The uncertainty principle: variations on a theme”, Bull. Amer. Math. Soc., 58:2 (2021), 225–261 | DOI | MR | Zbl