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Matematicheskie Zametki, 2011, Volume 90, Issue 4, Pages 483–500
DOI: https://doi.org/10.4213/mzm8585 (Mi mzm8585) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Continuity in $\Lambda$-Variation and Summation of Multiple Fourier Series by Cesàro Methods

A. N. Bakhvalov

M. V. Lomonosov Moscow State University
Full-text PDF (540 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm8585
Abstract: We construct new examples of functions of bounded $\Lambda$-variation not continuous in $\Lambda$-variation. Using these examples, we show that, in the problem of the summability of multiple Fourier series by the Cesàro method of negative order, the condition of continuity in $\Lambda$-variation, is essential in contrast to the one-dimensional case.
Keywords: multiple Fourier series, Cesàro mean, bounded variation, $\Lambda$-variation, Waterman class of functions, Pringsheim convergence.
Received: 25.11.2009
English version:
Mathematical Notes, 2011, Volume 90, Issue 4, Pages 469–484
DOI: https://doi.org/10.1134/S0001434611090185
Bibliographic databases:
Document Type: Article
UDC: 517.518
Language: Russian
Citation: A. N. Bakhvalov, “Continuity in $\Lambda$-Variation and Summation of Multiple Fourier Series by Cesàro Methods”, Mat. Zametki, 90:4 (2011), 483–500; Math. Notes, 90:4 (2011), 469–484
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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