Geodesic
On convergence of Fourier--Vilenkin series in $L^p[0,1)$, $0$
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 3, pp. 3-9.

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In this paper we study convergence a.e. and $L^p$-convergence ($0$) 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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S. S. Volosivets. On convergence of Fourier--Vilenkin series in $L^p[0,1)$, $0

[1] Golubov B. I., Efimov A. V., Skvortsov V. A., Ryady i preobrazovaniya Uolsha, Nauka, M., 1987 | MR | Zbl

[2] Moricz F., “Walsh–Fourier series with coefficients of generalized bounded variation”, J. Austral. Math. Soc. Ser. A, 47:3 (1989), 458–465 | DOI | MR | Zbl

[3] Moricz F., “On $L^1$-convergence of Walsh–Fourier series. II”, Acta Math. Hung., 58:1–2 (1991), 203–210 | DOI | MR | Zbl

[4] Agaev G. N., Vilenkin N. Ya., Dzhafarli G. M., Rubinshtein A. I., Multiplikativnye sistemy funktsii i garmonicheskii analiz na nul-mernykh gruppakh, Elm, Baku, 1981 | MR

[5] Pal J., Simon P., “On a generalization of the concept of derivative”, Acta Math. Hung., 29:1–2 (1977), 155–164 | DOI | MR | Zbl

[6] Moricz F., “On $L^1$-convergence of Walsh–Fourier series. I”, Rend. Circ. Mat. Palermo. Ser. 2, 38:3 (1989), 411–418 | DOI | MR | Zbl

[7] Chen C. P., “Pointwise convergence of trigonometric series”, J. Austral. Math. Soc. Ser. A, 43:2 (1987), 291–300 | DOI | MR | Zbl

[8] Stanojevic C. V., “Classes of $L^1$-convergence of Fourier and Fourier–Stieltjes series”, Proc. Amer. Math. Soc., 82:2 (1981), 209–215 | DOI | MR | Zbl

[9] Stanojevic C. V., “Tauberian conditions for $L^1$-convergence of Fourier series”, Trans. Amer. Math. Soc., 271:1 (1982), 237–244 | DOI | MR | Zbl