English

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

Classical Analysis and ODEs 2012-05-18 v1

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.

Keywords

Cite

@article{arxiv.1205.3973,
  title  = {On Ces\'aro summability of Fourier series of functions from multidimensional Waterman classes},
  author = {Alexandr Bakhvalov},
  journal= {arXiv preprint arXiv:1205.3973},
  year   = {2012}
}

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14 pages