Geodesic
$U$-convergence almost everywhere of double Fourier series
Sbornik. Mathematics, Tome 186 (1995) no. 1, pp. 47-64

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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. 
@article{SM_1995_186_1_a2,
     author = {M. I. Dyachenko},
     title = {$U$-convergence almost everywhere of double {Fourier} series},
     journal = {Sbornik. Mathematics},
     pages = {47--64},
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     volume = {186},
     number = {1},
     year = {1995},
     language = {en},
     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/