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Sharp Hausdorff--Young inequalities for some locally compact quantum groups
Abstract
In this paper, we show that the usual Hausdorff--Young inequalities for locally compact quantum groups such as the quantum Eq(2), the real quantum az+b, and the extended quantum SUq(1,1), where 0<q<1, are sharp. Moreover, there are no group-like projections with finite Haar weight in these locally compact quantum groups. We obtain a sharp Hausdorff--Young inequality for Kahng's skew-matrix quantum groups; the optimal constant is strictly less than one for 1<p<2; at p=2, Plancherel gives equality, and these quantum groups have no nonzero group-like projections with finite Haar weight.
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BibTeX
@misc{wu2026sharp,
title = {{Sharp Hausdorff--Young inequalities for some locally compact quantum groups}},
author = {Jinsong Wu and Fulin Yang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05863},
eprint = {2611.05863},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05863},
}
RIS
TY - UNPB
TI - Sharp Hausdorff--Young inequalities for some locally compact quantum groups
AU - Jinsong Wu
AU - Fulin Yang
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.05863
UR - https://arxiv.org/abs/2611.05863
AB - In this paper, we show that the usual Hausdorff--Young inequalities for locally compact quantum groups such as the quantum E_q(2), the real quantum az+b, and the extended quantum SU_q(1,1), where 0<q<1, are sharp. Moreover, there are no group-like projections with finite Haar weight in these locally compact quantum groups. We obtain a sharp Hausdorff--Young inequality for Kahng's skew-matrix quantum groups; the optimal constant is strictly less than one for 1<p<2; at p=2, Plancherel gives equality, and these quantum groups have no nonzero group-like projections with finite Haar weight.
ER -