The missing proof of Paley's theorem about lacunary coefficients

2014/07/06 by Fournier, John J. F.
#42B05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1407.1458

Abstract

We modify the standard proof of Paley's theorem about lacunary coefficients of functions in H¹ 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 L¹ norms of exponential sums.

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