The missing proof of Paley's theorem about lacunary coefficients

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 ex...

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Bibliographic Details
Published in:arXiv.org 2024-06
Main Author: Fournier, John J F
Format: Article
Language:English
Subjects:
Mathematical analysis
Norms
Theorem proving
Theorems
Online Access:Get full text
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Summary: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.
ISSN:2331-8422