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Sibirsk. Mat. Zh., 2017, Volume 58, Number 2, Pages 270–280 (Mi smj2858)  

On convergence of multiple trigonometric series with monotone coefficients

D. G. Dzhumabaevaa, M. I. Dyachenkob, E. D. Nursultanovc

a Gumilev Eurasian National University, Astana, Kazakhstan
b Lomonosov Moscow State University, Moscow, Russia
c Lomonosov Moscow State University, Kazakhstan Branch, Astana, Kazakhstan

Abstract: We study the Pringsheim pointwise convergence of multiple trigonometric series. We obtain a condition on the coefficients of the series that guarantees its Pringsheim convergence and prove the unimprovability of this condition.

Keywords: multiple trigonometric series, Pringsheim convergence, Lebesgue space with mixed metric, monotone coefficients.

Funding Agency Grant Number
Ministry of Education and Science of the Republic of Kazakhstan 4080/ГФ4
3311/ГФ4
Russian Foundation for Basic Research 15-01-01236
Ministry of Education and Science of the Russian Federation НШ-3682.2014.1
The first author was supported by the Ministry of Education and Science of the Republic of Kazakhstan (Grant 4080/GF4); the second author was supported by the Russian Foundation for Basic Research (Grant 15-01-01236); and the third author was supported by the Ministry of Education and Science of the Republic of Kazakhstan (Grants 4080/GF4 and 3311/GF4).


DOI: https://doi.org/10.17377/smzh.2017.58.203

Full text: PDF file (307 kB)
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English version:
Siberian Mathematical Journal, 2017, 58:2, 205–214

Bibliographic databases:

UDC: 517.51
MSC: 35R30
Received: 02.02.2016

Citation: D. G. Dzhumabaeva, M. I. Dyachenko, E. D. Nursultanov, “On convergence of multiple trigonometric series with monotone coefficients”, Sibirsk. Mat. Zh., 58:2 (2017), 270–280; Siberian Math. J., 58:2 (2017), 205–214

Citation in format AMSBIB
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\vol 58
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\pages 270--280
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