On everywhere divergence of the strong Φ-means of Walsh–Fourier series

Abstract

Almost everywhere strong exponential summability of Fourier series in Walsh and trigonometric systems was established by Rodin in 1990. We prove, that if the growth of a function Φ(t):[0,∞)→[0,∞) is bigger than the exponent, then the strong Φ-summability of a Walsh–Fourier series can fail everywhere. The analogous theorem for trigonometric system was proved before by one of the authors of this paper.