On a problem of Bourgain concerning the $$L^1$$ -norm of exponential sums
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Mathematische Zeitschrift
On a problem of Bourgain concerning the L 1 -norm of exponential sums Christoph Aistleitner
Received: 20 November 2012 / Accepted: 10 January 2013 © Springer-Verlag Berlin Heidelberg 2013
Abstract
Bourgain posed the problem of calculating n 1 2πik j θ = sup sup √ e n n≥1 k1 (log n)1/4 − c1 (log n)−3/4 − E|Z | √ π ≥ − c2 (log n)−1/16 . 2
for some appropriate constant c2 . Thus we have established (3), which proves Theorem 1.
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