A noncommutative maximal inequality for Fejér means on totally disconnected non-abelian groups
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911797865349120 |
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| author | Ding, Fugui Hong, Guixiang Wang, Xumin |
| author_facet | Ding, Fugui Hong, Guixiang Wang, Xumin |
| contents | In this paper, we explore Fourier analysis for noncommutative $L_p$ space-valued functions on $G$, where $G$ is a totally disconnected non-abelian compact group. By additionally assuming that the value of these functions remains invariant within each conjugacy class, we establish a noncommutative maximal inequality for Fejér means utilizing the associated character system of $G$. This is an operator-valued version of the classical result due to Gát. We follow essentially the classical sketch, but due to the noncommutativity, many classical arguments have to be revised. Notably, compared to the classical results. the bounds of our estimates are explicity calculated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09263 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A noncommutative maximal inequality for Fejér means on totally disconnected non-abelian groups Ding, Fugui Hong, Guixiang Wang, Xumin Functional Analysis 43A75, 42B25, 43A50 In this paper, we explore Fourier analysis for noncommutative $L_p$ space-valued functions on $G$, where $G$ is a totally disconnected non-abelian compact group. By additionally assuming that the value of these functions remains invariant within each conjugacy class, we establish a noncommutative maximal inequality for Fejér means utilizing the associated character system of $G$. This is an operator-valued version of the classical result due to Gát. We follow essentially the classical sketch, but due to the noncommutativity, many classical arguments have to be revised. Notably, compared to the classical results. the bounds of our estimates are explicity calculated. |
| title | A noncommutative maximal inequality for Fejér means on totally disconnected non-abelian groups |
| topic | Functional Analysis 43A75, 42B25, 43A50 |
| url | https://arxiv.org/abs/2403.09263 |