A Khintchine inequality for central Fourier series on non-Kac compact quantum groups
Abstract
The study of Khintchin inequalities has a long history in abstract harmonic analysis. While there is almost no possibility of non-trivial Khintchine inequality for central Fourier series on compact connected semisimple Lie groups, we demonstrate a strong contrast within the framework of compact quantum groups. Specifically, we establish a Khintchine inequality with operator coefficients for arbitrary central Fourier series in a large class of non-Kac compact quantum groups. The main examples include the Drinfeld-Jimbo $q$-deformations $G_q$, the free orthogonal quantum groups $O_F^+$, and the quantum automorphism group $G_{aut}(B,\psi)$ with a $\delta$-form $\psi$.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.13519
- arXiv:
- arXiv:2408.13519
- Bibcode:
- 2024arXiv240813519Y
- Keywords:
-
- Mathematics - Operator Algebras;
- Mathematics - Functional Analysis;
- 43A15;
- 46L67;
- 46L52;
- 47A30