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 
@article{MZM_2011_90_4_a0,
     author = {A. N. Bakhvalov},
     title = {Continuity in $\Lambda${-Variation} and {Summation} of {Multiple} {Fourier} {Series} by {Ces\`aro} {Methods}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {483--500},
     publisher = {mathdoc},
     volume = {90},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_4_a0/}
}
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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/