On the Hardy–Littlewood majorant problem for random sets

We study the classical Hardy–Littlewood majorant problem for trigonometric polynomials.We show that the constant in the majorant inequality grows at most like an arbitrary small power of the degree provided the spectrum is chosen at random. We also give an example of a deterministic set where the majorant property fails, i.e., the constant grows like a fixed small power in the degree. © 2008 Published by Elsevier Inc.