The missing proof of Paley's theorem about lacunary coefficients

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.

arXiv commentMore on related work. Many minor changes

Cited by in corpus (2)

• Discrete Fourier restriction theorems in two dimensions
• Noncommutative Khintchine and Paley inequalities via generic factorization