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An analogue of D. Waterman's result on the summability of the Fourier seriesfor functions of bounded \Lambda-variation by the Ces\'aro methods of negativeorder is obtained in multidimensional case. It is proved that, unlikeone-dimensional case, the continuity of function in the corresponding variationis essential for the convergence and even for the localization of the Ces\'aromeans for certain orders of these means.

On Ces\'aro summability of Fourier series of functions from multidimensional Waterman classes