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# Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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1337-2211
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# Almost everywhere convergence of some subsequences of Fejér means for integrable functions on some unbounded Vilenkin groups

Nacima Memić
Published Online: 2017-02-28 | DOI: https://doi.org/10.1515/ms-2016-0256

## Abstract

Following the methods of G. Gát, in this work we prove the a.e convergence of the subsequence $\begin{array}{}\left({\sigma }_{\frac{{m}_{n}}{2}{M}_{n}}f{\right)}_{n}\end{array}$, for every integrable function f on unbounded Vilenkin groups, such that the sequence (mn)n contains infinitely many even terms satisfying the estimate $\begin{array}{}\frac{\mathrm{ln}{m}_{k-1}\mathrm{ln}{m}_{k}}{{m}_{k}}=O\left(1\right).\end{array}$

MSC 2010: Primary 42C10

## References

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Gát, G.: Almost everywhere convergence of Fejér means of L1 functions on rarely unbounded Vilenkin groups, Acta Math. Sin. 23 (2007), 2269–2294.Google Scholar

• [2]

Gát, G.: Cesàro means of integrable functions with respect to unbounded Vilenkin systems, J. Approx. Theory. 124 (2003), 25–43.Google Scholar

• [3]

Gát, G.: Pointwise convergence of the Fejér means of functions on unbounded Vilenkin groups, J. Approx. Theory. 101 (1999), 1–36.Google Scholar

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Pál, J.—Simon, P.: On a generalization of the concept of derivative, Acta Math. Acad. Sci. Hungar. 29 (1977), 155–164.Google Scholar

• [5]

Young, W. S.: Mean convergence of generalized Walsh-Fourier series, Trans. Amer. Math. Soc. 218 (1976), 311–320.Google Scholar

Accepted: 2015-01-23

Published Online: 2017-02-28

Published in Print: 2017-02-01

Citation Information: Mathematica Slovaca, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918,

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