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 Ural Math. J., 2017, Volume 3, Issue 2, Pages 14–21 (Mi umj38)

On $\Lambda$-convergence almost everywhere of multiple trigonometric Fourier series

Nikolai Yu. Antonov

Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: We consider one type of convergence of multiple trigonometric Fourier series intermediate between the convergence over cubes and the $\lambda$-convergence for $\lambda >1$. The well-known result on the almost everywhere convergence over cubes of Fourier series of functions from the class $L (\ln ^ + L) ^ d \ln ^ + \ln ^ + \ln ^ + L ([0,2 \pi)^d )$ has been generalized to the case of the $\Lambda$-convergence for some sequences $\Lambda$.

Keywords: Trigonometric Fourier series, Rectangular partial sums, Convergence almost everywhere.

 Funding Agency Grant Number Russian Science Foundation 14-11-00702 This work was supported by the Russian Science Foundation (project no. 14-11-00702).

DOI: https://doi.org/10.15826/umj.2017.2.003

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Citation: Nikolai Yu. Antonov, “On $\Lambda$-convergence almost everywhere of multiple trigonometric Fourier series”, Ural Math. J., 3:2 (2017), 14–21

Citation in format AMSBIB
\Bibitem{Ant17} \by Nikolai~Yu.~Antonov \paper On $\Lambda$-convergence almost everywhere of multiple trigonometric Fourier series \jour Ural Math. J. \yr 2017 \vol 3 \issue 2 \pages 14--21 \mathnet{http://mi.mathnet.ru/umj38} \crossref{https://doi.org/10.15826/umj.2017.2.003}