A remark on the divergence of strong power means of Walsh-Fourier series

G. Gát; U. Goginava; G. Karagulyan

doi:10.1134/S0001434614110261

A remark on the divergence of strong power means of Walsh-Fourier series

G. Gát
, U. Goginava
, G. Karagulyan

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

2 Citations (Scopus)

Abstract

F. Schipp in 1969 proved the almost everywhere p-strong summability of Walsh-Fourier series and showed that if λ(n)→∞, then there exists a function f ∈ L₁[0, 1) for which the Walsh partial sums S_k(x, f) satisfy the divergence condition (Formula Presented.) almost everywhere on [0, 1). In the present paper, we show that this condition holds everywhere.

Original language	English
Pages (from-to)	897-903
Number of pages	7
Journal	Mathematical Notes
Volume	96
Issue number	5-6
DOIs	https://doi.org/10.1134/S0001434614110261
Publication status	Published - 2014
Externally published	Yes

Keywords

everywhere divergent Walsh-Fourier series
strong summability
Walsh series

ASJC Scopus subject areas

General Mathematics

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10.1134/S0001434614110261

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abstract = "F. Schipp in 1969 proved the almost everywhere p-strong summability of Walsh-Fourier series and showed that if λ(n)→∞, then there exists a function f ∈ L1[0, 1) for which the Walsh partial sums Sk(x, f) satisfy the divergence condition (Formula Presented.) almost everywhere on [0, 1). In the present paper, we show that this condition holds everywhere.",

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AU - Karagulyan, G.

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N2 - F. Schipp in 1969 proved the almost everywhere p-strong summability of Walsh-Fourier series and showed that if λ(n)→∞, then there exists a function f ∈ L1[0, 1) for which the Walsh partial sums Sk(x, f) satisfy the divergence condition (Formula Presented.) almost everywhere on [0, 1). In the present paper, we show that this condition holds everywhere.

AB - F. Schipp in 1969 proved the almost everywhere p-strong summability of Walsh-Fourier series and showed that if λ(n)→∞, then there exists a function f ∈ L1[0, 1) for which the Walsh partial sums Sk(x, f) satisfy the divergence condition (Formula Presented.) almost everywhere on [0, 1). In the present paper, we show that this condition holds everywhere.

KW - everywhere divergent Walsh-Fourier series

KW - strong summability

KW - Walsh series

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ER -

A remark on the divergence of strong power means of Walsh-Fourier series

Abstract

Keywords

ASJC Scopus subject areas

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