Geodesic
On the growth order of sequences of double rectangular Fourier sums for functions from the classes $\varphi(L)$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 26-34 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain estimates for the growth order of arbitrary sequences of rectangular partial sums of double trigonometric Fourier series for functions from the classes $\varphi(L)$, which are intermediate between $L\log^+L_{[0,2\pi)^2}$; and $L(\log^+L)^2_{[0,2\pi)^2}$.
Keywords: multiple trigonometric Fourier series, growth order estimates. 
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N. Yu. Antonov. On the growth order of sequences of double rectangular Fourier sums for functions from the classes $\varphi(L)$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 26-34. http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a2/

[1] Hardy G. H., “On the summability of Fourier series”, Proc. London Math. Soc., 12 (1913), 365–372 | DOI | Zbl

[2] Oskolkov K. I., “Podposledovatelnosti summ Fure integriruemykh funktsii”, Tr. MIAN, 167, 1985, 239–260 | MR | Zbl

[3] Karagulyan G. A., “Preobrazovanie Gilberta i eksponentsialnye integralnye otsenki pryamougolnykh chastichnykh summ dvoinykh ryadov Fure”, Mat. sb., 187:3 (1996), 55–74 | DOI | MR | Zbl

[4] Antonov N. Yu., “O skorosti rosta proizvolnykh posledovatelnostei dvoinykh pryamougolnykh summ Fure”, Tr. In-ta matematiki i mekhaniki UrO RAN, 16, no. 4, 2010, 31–37

[5] Antonov N. Yu., “Conditions for the finiteness of majorants for sequences of operators and convergence of Fourier series”, Proc. Steklov Inst. Math., 2001, S1–S19 | MR | Zbl

[6] Stein E. M., “On limits of sequences of operators”, Ann. Math., 74:1 (1961), 140–170 | DOI | MR | Zbl

[7] Sjölin P., “An inequality of Paley and convergence a. e. of Walsh-Fourier series”, Arkiv för Mat., 7 (1969), 551–570 | DOI | MR

[8] Hunt R. A., “On the convergence of Fourier series”, Orthogonal Expansions and their Continuous Analogues, Proc. Conf., SIU Press, Carbondale, 1968, 235–255 | MR