Geodesic
On $\Lambda$-convergence almost everywhere of multiple trigonometric Fourier series
Ural mathematical journal, Tome 3 (2017) no. 2, pp. 14-21

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We consider one type of convergence of multiple trigonometric Fourier series intermediate between the convergence over cubes and the $\lambda $-convergence for $\lambda >1$. The well-known result on the almost everywhere convergence over cubes of Fourier series of functions from the class $ L (\ln ^ + L) ^ d \ln ^ + \ln ^ + \ln ^ + L ([0,2 \pi)^d ) $ has been generalized to the case of the $ \Lambda $-convergence for some sequences $\Lambda$.
Keywords: Trigonometric Fourier series, Rectangular partial sums, Convergence almost everywhere. 
@article{UMJ_2017_3_2_a2,
     author = {Nikolai Yu. Antonov},
     title = {On $\Lambda$-convergence almost everywhere of multiple trigonometric {Fourier} series},
     journal = {Ural mathematical journal},
     pages = {14--21},
     publisher = {mathdoc},
     volume = {3},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2017_3_2_a2/}
}
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Nikolai Yu. Antonov. On $\Lambda$-convergence almost everywhere of multiple trigonometric Fourier series. Ural mathematical journal, Tome 3 (2017) no. 2, pp. 14-21. http://geodesic.mathdoc.fr/item/UMJ_2017_3_2_a2/