Geodesic
Strong means and oscillation of multiple Fourier series in multiplicative systems
Matematičeskie zametki, Tome 63 (1998) no. 4, pp. 607-616.

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In this paper we establish a general assertion relating the oscillation of the sequence of rectangular partial sums of a multiple Fourier series in a multiplicative system to the strong summability of this series. The systems of group generators are assumed to be uniformly bounded. Earlier these assertions were obtained by the author for the Walsh and Chrestenson series. 
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     author = {V. A. Rodin},
     title = {Strong means and oscillation of multiple {Fourier} series in multiplicative systems},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_4_a13/}
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V. A. Rodin. Strong means and oscillation of multiple Fourier series in multiplicative systems. Matematičeskie zametki, Tome 63 (1998) no. 4, pp. 607-616. http://geodesic.mathdoc.fr/item/MZM_1998_63_4_a13/

[1] Schipp F., “Bemerkung zur starken Summation der Walsh–Fourier–Reihe”, Acta Math. Hungar., 20:3–4 (1969), 263–274 | MR | Zbl

[2] Edvards R., Ryady Fure v sovremennom izlozhenii, T. 1, Mir, M., 1985

[3] Rodin V. A., “The space BMO and strong means of Fourier series”, Anal. Math., 16:4 (1990), 291–302 | DOI | MR | Zbl

[4] Rodin V. A., “Prostranstvo BMO i silnye srednie ryada Fure–Uolsha”, Matem. sb., 182:10 (1991), 1463–1478

[5] Rodin V. A., “Totik's conjecture for Chrestenson and Walsh systems”, Anal. Math., 18:4 (1992), 295–305 | DOI | MR | Zbl

[6] Rodin V. A., “BMO-svoistva chastichnykh summ ryada Fure”, Dokl. AN SSSR, 319:5 (1991), 1079–1081 | MR | Zbl

[7] Garnet Dzh., Ogranichennye analiticheskie funktsii, Mir, M., 1984 | Zbl

[8] Agaev G. N., Vilenkin N. Ya., Dzhafarli G. M., Rubinshtein A. I., Multiplikativnye sistemy funktsii i garmonicheskii analiz na nulmernykh gruppakh, ELM, Baku, 1981

[9] Gabisoniya O. D., “O tochkakh silnoi summiruemosti ryadov Fure”, Matem. zametki, 14 (1973), 615–626 | MR

[10] Zigmund A., Trigonometricheskie ryady, T. 2, Mir, M., 1965

[11] Stein E. M., “On limits of sequences of operators”, Ann. of Math. (2), 74 (1961), 140–170 | DOI | MR | Zbl

[12] Kashin B. S., Saakyan A. A., Ortogonalnye ryady, Nauka, M., 1984 | Zbl