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arXiv · 1205.3973

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

Alexandr Bakhvalov
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Abstract

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

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Alexandr Bakhvalov. 2012-05-17. On Ces\'aro summability of Fourier series of functions from multidimensional Waterman classes. https://arxiv.org/abs/1205.3973

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