Geodesic
Trigonometric series with lacunary-monotone coefficients
Eurasian mathematical journal, Tome 3 (2012) no. 2, pp. 31-52.

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In this paper we study multiple trigonometric series with lacunary-monotone coefficients. We obtain necessary and sufficient conditions for the sum of such series to belong to $L_p$, $1$ and the generalized Lipschitz spaces (Nikol'skii spaces). 
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M. I. Dyachenko; S. Tikhonov. Trigonometric series with lacunary-monotone coefficients. Eurasian mathematical journal, Tome 3 (2012) no. 2, pp. 31-52. http://geodesic.mathdoc.fr/item/EMJ_2012_3_2_a3/

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