D. G. Dzhumabaeva, M. I. Dyachenko, E. D. Nursultanov, “On convergence of multiple trigonometric series with monotone coefficients”, Sibirsk. Mat. Zh., 2017, Volume 58, Number 2,Pages <nobr>270

This article is cited in 3 papers

On convergence of multiple trigonometric series with monotone coefficients

D. G. Dzhumabaeva^a, M. I. Dyachenko^b, E. D. Nursultanov^c

^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.

UDC: 517.51

MSC: 35R30

Received: 02.02.2016

DOI: 10.17377/smzh.2017.58.203