Lacunary Fourier and Walsh-Fourier series near \(L^1\) (Q486336)

The author of the article under review proves that for a lacunary sequence \(\{n_j\}\) and for a continuous function \(f\) on the unit circle, the subsequences \(F_{n_j}f\) and \(W_{n_j}f\) of the Fourier series and Walsh series converge to \(f\) almost everywhere under an integral condition on \(f\) that involves the quadruple logarithm.