Geodesic
Properties of sums of double trigonometric series with multiply monotone coefficients
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2020), pp. 8-22 
T. M. Vukolova; B. V. Simonov. Properties of sums of double trigonometric series with multiply monotone coefficients. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2020), pp. 8-22. http://geodesic.mathdoc.fr/item/VMUMM_2020_5_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Sums of double sine and cosine series with multiply monotonic coefficients are studied. Sufficient conditions for such sums to belong to Orlich's weighted classes are obtained.

[1] Uitteker E.T., Vatson Dzh.N., Kurs sovremennogo analiza, v. 1, Fizmatgiz, M., 1962

[2] Vukolova T.M., Dyachenko M.I., “Otsenki smeshannykh norm summ dvoinykh trigonometricheskikh ryadov s kratno monotonnymi koeffitsientami”, Izv. vuzov. Matematika, 1997, no. 7, 3–13

[3] Bari N.K., Stechkin S.B., “Nailuchshie priblizheniya i differentsialnye svoistva dvukh sopryazhennykh funktsii”, Tr. Mosk. mat. o-va, 5, 1956, 483–521

[4] Simonov B.V., “O ryadakh po sinusam i kosinusam v klassakh $L_\varphi$”, Izv. vuzov. Matematika, 2013, no. 10, 24–42