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arXiv · 1312.0855

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

G. Gát·U. Goginava·G. Karagulyan
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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.

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G. Gát, U. Goginava, G. Karagulyan. 2013-12-03. On everywhere divergence of the strong $\Phi$-means of Walsh-Fourier series. https://doi.org/10.1016/j.jmaa.2014.07.016

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