Geodesic
$U$-convergence almost everywhere of double Fourier series
Sbornik. Mathematics, Tome 186 (1995) no. 1, pp. 47-64 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we consider $u$-convergence of double Fourier series ($u$-convergence of a double number series implies that it converges in the sense of Pringsheim, over spheres, and so on.) Unextendable classes of Weyl multipliers for $u$-convergence almost everywhere are described. In addition, close to exact sufficient conditions for $u$-convergence almost everywhere in the spaces $L(T^2)$ and $L_2(T^2)$ are found. 
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     title = {$U$-convergence almost everywhere of double {Fourier} series},
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     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_1_a2/}
}
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M. I. Dyachenko. $U$-convergence almost everywhere of double Fourier series. Sbornik. Mathematics, Tome 186 (1995) no. 1, pp. 47-64. http://geodesic.mathdoc.fr/item/SM_1995_186_1_a2/

[1] Arutyunyan F. G., “Predstavlenie funktsii kratnymi ryadami”, DAN Arm. SSR, 64:2 (1977), 72–76 | MR | Zbl

[2] Arutyunyan F. G., “Predstavlenie izmerimykh funktsii mnogikh peremennykh kratnymi trigonometricheskimi ryadami”, Matem. sb., 126:2 (1985), 267–285 | MR | Zbl

[3] Dyachenko M. I., “Nekotorye problemy teorii kratnykh trigonometricheskikh ryadov”, UMN, 47:5 (1992), 97–162 | MR | Zbl

[4] Dyachenko M. I., “$U$-skhodimost kratnykh ryadov Fure”, Izv. RAN. Seriya matem. (to appear)

[5] Sjolin P., “Convergence almost everywhere of certain singular integrals and multiple Fourier series”, Ark. mat., 9:1 (1971), 65–90 | DOI | MR

[6] Nikishin E. M., “Mnozhiteli Veilya dlya kratnykh ryadov Fure”, Matem. sb., 89:2 (1972), 340–348 | MR | Zbl

[7] Ulyanov P. L., “O nekotorykh ekvivalentnykh usloviyakh skhodimosti ryadov i integralov”, UMN, 8:6 (1953), 133–141 | MR | Zbl

[8] Golubov B. I., “O skhodimosti sfericheskikh srednikh Rissa kratnykh ryadov Fure”, Matem. sb., 96(138):2 (1975), 189–211 | MR | Zbl

[9] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977 | MR

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