Geodesic
Estimates of quasi-norms for a certain class of double sine series
Contemporary Mathematics and Its Applications, Tome 96 (2015), pp. 132-142.

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It this paper, we examine the sums of double sine series with coefficients that are multiply monotonic with respect to subsequences. We obtain sufficient conditions under which these sums belong to the classes $L_p$, $0$. 
@article{CMA_2015_96_a8,
     author = {B. V. Simonov and I. E. Simonova},
     title = {Estimates of quasi-norms for a certain class of double sine series},
     journal = {Contemporary Mathematics and Its Applications},
     pages = {132--142},
     publisher = {mathdoc},
     volume = {96},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMA_2015_96_a8/}
}
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B. V. Simonov; I. E. Simonova. Estimates of quasi-norms for a certain class of double sine series. Contemporary Mathematics and Its Applications, Tome 96 (2015), pp. 132-142. http://geodesic.mathdoc.fr/item/CMA_2015_96_a8/