Geodesic
On the convergence of double trigonometric series and Fourier series with monotone coefficients
Sbornik. Mathematics, Tome 57 (1987) no. 1, pp. 57-75 
M. I. Dyachenko. On the convergence of double trigonometric series and Fourier series with monotone coefficients. Sbornik. Mathematics, Tome 57 (1987) no. 1, pp. 57-75. http://geodesic.mathdoc.fr/item/SM_1987_57_1_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The author studies some questions about the way in which the convergence of double trigonometric series depends on the properties of the coefficients. Bibliography: 11 titles.

[1] Bari N. K, Trigonometricheskie ryady, Fizmatgiz, M., 1961 | MR

[2] Polia G., Sege G., Zadachi i teoremy iz analiza, T. 1, Nauka, M., 1978

[3] Dyachenko M. I., “O trigonometricheskikh ryadakh s monotonnymi koeffitsientami”, Vsesoyuznaya shkola po teorii funktsii, posvyaschennaya 100-letiyu so dnya rozhdeniya akademika N. N. Luzina (Tezisy dokladov), Kemerovo, 1983, 42

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[5] Zygmund A., “On a theorem of Hadamard”, Ann. Soc. Polon. Math., 21 (1948), 52–69 | MR | Zbl

[6] Rudin W., “Some theorems on Fourier coefficients”, Proc. Amer. Math. Soc., 10 (1959), 855–859 | DOI | MR | Zbl

[7] Brillhart J., Carlitz L., “Note on the Shapiro polynomials”, Proc. Amer. Math. Soc., 25 (1970), 114–118 | DOI | MR | Zbl

[8] Kaczmarz S., “Sur theory der Fourierschen Doppelreihen”, Studia Math., 2 (1930), 91–96 | Zbl

[9] Tevzadze N. R., “O skhodimosti dvoinogo ryada Fure funktsii, summiruemoi s kvadratom”, Soobsch. AN GruzSSR, 58 (1970), 277–279 | MR | Zbl

[10] Baiborodov S. P., “Konstanty Lebega mnogogrannikov”, Matem. zametki, 32 (1982), 817–822 | MR | Zbl

[11] Sokol-Sokolowski K., “On trigonometric series conjugate to Fourier series of two variables”, Fund. Math., 34 (1947), 166–182 | MR | Zbl