Geodesic
Asymptotics of multiple trigonometric series with monotone coefficients
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2015), pp. 14-22

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The paper describes a general method of determination of the asymptotic behavior near zero of multiple trigonometric series whose coefficients possess certain monotonicity conditions. 
@article{VMUMM_2015_6_a2,
     author = {A. Zh. Ydyrys},
     title = {Asymptotics of multiple trigonometric series with monotone coefficients},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {14--22},
     publisher = {mathdoc},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2015_6_a2/}
}
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A. Zh. Ydyrys. Asymptotics of multiple trigonometric series with monotone coefficients. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2015), pp. 14-22. http://geodesic.mathdoc.fr/item/VMUMM_2015_6_a2/