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

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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. 
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/
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