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arXiv · 2610.01561

Sharp higher-order uncertainty principles

Hongtao Hu·Meiqi Liu·Wenming Zou
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Abstract

We establish a class of sharp higher-order inequalities related to the uncertainty principle. First, by means of the expanding the squares method, we give a concise proof of sharp higher-order Heisenberg uncertainty principles. We provide explicit expressions for the optimal constants and establish the existence of extremal functions. Furthermore, we obtain sharp higher-order Heisenberg uncertainty principles for curl-free vector fields. In particular, when $N=2$, we give an answer to the higher-order version of Open Problem 9 raised by Maz'ya in [Integr. Equ. Oper. Theory (2018) 90:25]. Second, we establish sharp higher-order Heisenberg uncertainty principles that do not involve higher-order tensors. We also prove sharp higher-order Heisenberg uncertainty principles and higher-order hydrogen uncertainty principles for radially symmetric functions.

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Hongtao Hu, Meiqi Liu, Wenming Zou. 2026-10-01. Sharp higher-order uncertainty principles. https://arxiv.org/abs/2610.01561

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