Abstract:
Let two classes $(\Lambda^1,\dots,\Lambda^m)BV$ and $(M^1,\dots,M^m)BV$ on an interval $\Delta$ be given. In the paper, we find necessary and sufficient conditions for the $\Lambda$-variation of any function in the $M$-class, over a neighbourhood of every regular point, to tend to zero as the neighbourhood decreases.
Bibliography: 10 titles.
Keywords:
generalized variation, regular point, variation over a neighbourhood.
\Bibitem{Bak10}
\by A.~N.~Bakhvalov
\paper On the local behaviour of the multidimensional $\Lambda$-variation
\jour Sb. Math.
\yr 2010
\vol 201
\issue 11
\pages 1563--1578
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Linking options:
https://www.mathnet.ru/eng/sm7634
https://doi.org/10.1070/SM2010v201n11ABEH004122
https://www.mathnet.ru/eng/sm/v201/i11/p3
This publication is cited in the following 3 articles:
Alexandr N. Bakhvalov, “On certain integral means of functions of generalized bounded variation”, Georgian Mathematical Journal, 28:2 (2021), 185
Olevskyi V., Olevska Yu., “Geometric Aspects of Multiple Fourier Series Convergence on the System of Correctly Counted Sets”, Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization, eds. Mladenov I., Yoshioka A., Inst Biophysics & Biomedical Engineering Bulgarian Acad Sciences, 2018, 159–167
Bakhvalov A.N., “Cesaro summation of Fourier series of functions from multidimensional Waterman classes”, Dokl. Math., 83:2 (2011), 247–249
Citation in format AMSBIB
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