The missing proof of Paley's theorem about lacunary coefficients
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2014
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866913406763663360 |
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| author | Fournier, John J. F. |
| author_facet | Fournier, John J. F. |
| contents | We modify the standard proof of Paley's theorem about lacunary coefficients of functions in $H^1$ to work without analytic factorization. This leads to the first direct proof of the extension of Paley's theorem that we applied to the former Littlewood conjecture about $L^1$ norms of exponential sums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1407_1458 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | The missing proof of Paley's theorem about lacunary coefficients Fournier, John J. F. Classical Analysis and ODEs 42B05 We modify the standard proof of Paley's theorem about lacunary coefficients of functions in $H^1$ to work without analytic factorization. This leads to the first direct proof of the extension of Paley's theorem that we applied to the former Littlewood conjecture about $L^1$ norms of exponential sums. |
| title | The missing proof of Paley's theorem about lacunary coefficients |
| topic | Classical Analysis and ODEs 42B05 |
| url | https://arxiv.org/abs/1407.1458 |