A Khintchine inequality for central Fourier series on non-Kac compact quantum groups
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914922461396992 |
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| author | Youn, Sang-Gyun |
| author_facet | Youn, Sang-Gyun |
| contents | 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 $G_{aut}(B,ψ)$ with a $δ$-form $ψ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13519 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Khintchine inequality for central Fourier series on non-Kac compact quantum groups Youn, Sang-Gyun Operator Algebras Functional Analysis 43A15, 46L67, 46L52, 47A30 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 $G_{aut}(B,ψ)$ with a $δ$-form $ψ$. |
| title | A Khintchine inequality for central Fourier series on non-Kac compact quantum groups |
| topic | Operator Algebras Functional Analysis 43A15, 46L67, 46L52, 47A30 |
| url | https://arxiv.org/abs/2408.13519 |