Almost uniform convergence for noncommutative Vilenkin-Fourier series
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909651498434560 |
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| author | Jiao, Yong Luo, Sijie Zhao, Tiantian Zhou, Dejian |
| author_facet | Jiao, Yong Luo, Sijie Zhao, Tiantian Zhou, Dejian |
| contents | In the present paper, we study almost uniform convergence for noncommutative Vilenkin-Fourier series. Precisely, we establish several noncommutative (asymmetric) maximal inequalities for the Cesàro means of the noncommutative Vilenkin-Fourier series, which in turn give the corresponding almost uniform convergence. The primary strategy in our proof is to explore a noncommutative generalization of Sunouchi square function operator, and the very recent advance of the noncommutative Calderón-Zygmund decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14431 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Almost uniform convergence for noncommutative Vilenkin-Fourier series Jiao, Yong Luo, Sijie Zhao, Tiantian Zhou, Dejian Functional Analysis Primary 46L52, Secondary 42B20, 46L53 In the present paper, we study almost uniform convergence for noncommutative Vilenkin-Fourier series. Precisely, we establish several noncommutative (asymmetric) maximal inequalities for the Cesàro means of the noncommutative Vilenkin-Fourier series, which in turn give the corresponding almost uniform convergence. The primary strategy in our proof is to explore a noncommutative generalization of Sunouchi square function operator, and the very recent advance of the noncommutative Calderón-Zygmund decomposition. |
| title | Almost uniform convergence for noncommutative Vilenkin-Fourier series |
| topic | Functional Analysis Primary 46L52, Secondary 42B20, 46L53 |
| url | https://arxiv.org/abs/2506.14431 |