Year: 2026
Type: preprint
Abstract: We prove the sharp Hausdorff--Young inequality on quantum euclidean spaces. Our result implies the sharp Hausdorff--Young constants for the Weyl transform. The key ingredients are a sharp Hessian comparison inequality and a novel flow related to the mixed- norm of noncommutative Gabor transform; the Hessian comparison leads to the monotonicity of the flow. We also apply the same flow technique to prove the sharp Hausdorff--Young inequalities on Heisenberg groups and the affine group.
Source: arXiv (Cornell University)
Authors: Qiu, Hongsen, Xiong, Xiao
Institution: Harbin Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1611165156, G7944262688
OpenAlex ID: W7212182999