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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, Volume 14, Issue 4(2), Pages 497–505
DOI: https://doi.org/10.18500/1816-9791-2014-14-4-497-505 (Mi isu541) 		 
Mathematics

On Divergence Almost Everywhere of Fourier Series of Continuous Functions of Two Variables

N. Yu. Antonov

N. N. Krasovskii Institute of Mathematics and Mechanics UB RAS, 16, S. Kovalevskoy str., Ekaterinburg, 620990, Russia
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DOI: https://doi.org/10.18500/1816-9791-2014-14-4-497-505
Abstract: We consider one type of convergence of double trigonometric Fourier series intermediate between convergence over squares and $\lambda$-convergence for $\lambda>1$. We construct an example of continuous functions of two variables, Fourier series of which diverges in this sense, almost everywhere.
Key words: multiple Fourier series, almost everywhere convergence.
Bibliographic databases:
Document Type: Article
UDC: 517.518
Language: Russian
Citation: N. Yu. Antonov, “On Divergence Almost Everywhere of Fourier Series of Continuous Functions of Two Variables”, Izv. Saratov Univ. Math. Mech. Inform., 14:4(2) (2014), 497–505
Citation in format AMSBIB
\Bibitem{Ant14}
\by N.~Yu.~Antonov
\paper On Divergence Almost Everywhere of Fourier Series of Continuous Functions of Two Variables
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2014
\vol 14
\issue 4(2)
\pages 497--505
\mathnet{http://mi.mathnet.ru/isu541}
\crossref{https://doi.org/10.18500/1816-9791-2014-14-4-497-505}
\elib{https://elibrary.ru/item.asp?id=22625598}
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    		Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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