An Example of the Sequence of Coefficients of a Double Trigonometric Series

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.