On Cesáro summability of Fourier series of functions from multidimensional Waterman classes
An analogue of D. Waterman's result on the summability of the Fourier series for functions of bounded Λ-variation by the Cesáro 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 Cesáro means for certain orders of these means.
math.CA↗