On the Order of Fourier Coefficients of a Lacunary Fourier Series

Let ∑ (an_k con n_kx + b_nk sin n_kx) be the Fourier series of a 2π-periodic function f ∈ L [—π, π] with an infinity of gaps (n_k, n_k+1) where {n_k} (k∈ N ) is a strictly increasing sequence of natural numbers.