Geodesic
Continuity in $\Lambda$-Variation and Summation of Multiple Fourier Series by Ces\`aro Methods
Matematičeskie zametki, Tome 90 (2011) no. 4, pp. 483-500.

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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, Waterman class of functions, Pringsheim convergence.
Mots-clés : $\Lambda$-variation 
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A. N. Bakhvalov. Continuity in $\Lambda$-Variation and Summation of Multiple Fourier Series by Ces\`aro Methods. Matematičeskie zametki, Tome 90 (2011) no. 4, pp. 483-500. http://geodesic.mathdoc.fr/item/MZM_2011_90_4_a0/

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