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

G. Gát; U. Goginava; G. Karagulyan

doi:10.1016/j.jmaa.2014.07.016

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

G. Gát
, U. Goginava
, G. Karagulyan

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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.

Original language	English
Pages (from-to)	206-214
Number of pages	9
Journal	Journal of Mathematical Analysis and Applications
Volume	421
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2014.07.016
Publication status	Published - Jan 1 2015
Externally published	Yes

Keywords

Everywhere divergent Walsh-Fourier series
Strong summability
Walsh series

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2014.07.016

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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.",

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AU - Karagulyan, G.

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N2 - 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.

AB - 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.

KW - Everywhere divergent Walsh-Fourier series

KW - Strong summability

KW - Walsh series

UR - https://www.scopus.com/pages/publications/84919946768

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

Abstract

Keywords

ASJC Scopus subject areas

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