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arXiv · 1407.1458

The missing proof of Paley's theorem about lacunary coefficients

John J. F. Fournier
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Abstract

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.

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John J. F. Fournier. 2014-07-06. The missing proof of Paley's theorem about lacunary coefficients. https://arxiv.org/abs/1407.1458

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