Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Volosivets S. S. On Convergence of Fourier – Vilenkin Series in L p [0, 1), 0 < p ≤ 1. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2008, vol. 8, iss. 3, pp. 3-9. DOI: 10.18500/1816-9791-2008-8-3-3-9

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
16.06.2008
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Language: 
Russian
Heading: 
Mathematics
UDC: 
517.518
DOI: 
10.18500/1816-9791-2008-8-3-3-9

On Convergence of Fourier – Vilenkin Series in L p [0, 1), 0 < p ≤ 1

Autors: 
Volosivets Sergei Sergeevich, Saratov State University
Abstract: 

In this paper we study convergence a.e. and L p -convergence (0 < p ≤ 1) of Fourier –Vilenkin series under some tauberian conditions on Fourier coefficients of a function. In the case of Fourier – Walsh series these results are obtained by F. Moricz.

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References: 
  1. Голубов Б.И., Ефимов А.В., Скворцов В.А. Ряды и преобразования Уолша. М.: Наука, 1987.
  2. Moricz F. Walsh – Fourier series with coefficients of generalized bounded variation // J. Austral. Math. Soc. Ser. A. 1989. V. 47, No 3. P. 458–465.
  3. Moricz F. On L 1-convergence of Walsh – Fourier series. II. // Acta Math. Hung. 1991. V. 58, No 1–2. P. 203–210.
  4. Агаев Г.Н., Виленкин Н.Я., Джафарли Г.М., Рубинштейн А.И. Мультипликативные системы функций и гармонический анализ на нуль-мерных группах. Баку: Элм, 1981.
  5. Pal J., Simon P. On a generalization of the concept of derivative // Acta Math. Hung. 1977. V.29, No 1–2. P. 155–164.
  6. Moricz F. On L -convergence of Walsh – Fourier series. I. // Rend. Circ. Mat. Palermo. Ser. 2. 1989. V.38, No 3. P.411–418.
  7. Chen C.P. Pointwise convergence of trigonometric series // J. Austral. Math. Soc. Ser. A. 1987. V.43, No 2. P. 291–300.
  8. Stanojevic C.V. Classes of L 1-convergence of Fourier and Fourier – Stieltjes series // Proc. Amer. Math. Soc. 1981. V. 82, No 2. P. 209–215.
  9. Stanojevic C.V. Tauberian conditions for L 1-convergence of Fourier series // Trans. Amer. Math. Soc. 1982. V.271, No 1. P. 237–244.
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