On everywhere divergence of the strong $\Phi$-means of Walsh-Fourier series

Abstract

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

arXiv comment8 pages