Geodesic
An Example of the Sequence of Coefficients of a Double Trigonometric Series
Matematičeskie zametki, Tome 90 (2011) no. 1, pp. 45-52

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We construct an example of a double sequence $a$ of nonnegative numbers that are monotone decreasing to zero in the first index for any fixed value of the second index and two Hadamard lacunary sequences of natural numbers such that the double trigonometric lacunary monotone series with the coefficients $a$ constructed from the first lacunary sequence is square-divergent almost everywhere and the one constructed from the second lacunary sequence is square-convergent almost everywhere.
Keywords: double trigonometric series, Hadamard lacunary sequence, square-convergent series, lacunary monotone coefficient, Pringsheim convergence, Fourier series. 
@article{MZM_2011_90_1_a5,
     author = {M. I. Dyachenko},
     title = {An {Example} of the {Sequence} of {Coefficients} of a {Double} {Trigonometric} {Series}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {45--52},
     publisher = {mathdoc},
     volume = {90},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_1_a5/}
}
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M. I. Dyachenko. An Example of the Sequence of Coefficients of a Double Trigonometric Series. Matematičeskie zametki, Tome 90 (2011) no. 1, pp. 45-52. http://geodesic.mathdoc.fr/item/MZM_2011_90_1_a5/