A Khintchine inequality for central Fourier series on non-Kac compact quantum groups

Sang-Gyun Youn
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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 $\psi$.
非 Kac 紧凑量子群上中心傅里叶级数的 Khintchine 不等式
辛钦不等式的研究在抽象调和分析中由来已久。虽然在紧凑相连的半简单李群上几乎不可能存在中心傅里叶级数的非难Khintchine不等式,但我们在紧凑量子群的框架内证明了一个强烈的对比。具体地说,我们为一大类非 Kac 紧凑量子群中的任意中心傅里叶级数建立了带操作系数的 Khintchine 不等式。主要例子包括 Drinfeld-Jimbo$q$ 变形 $G_q$、自由正交量子群 $O_F^+$,以及具有 $\delta$ 形式 $\psi$ 的量子自变群 $G_{aut}(B,\psi)$。
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