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Mat. Sb. (N.S.), 1979, Volume 109(151), Number 2(6), Pages 291–326 (Mi msb2377)  

This article is cited in 1 scientific paper (total in 1 paper)

Functions of bounded generalized second variation

T. I. Akhobadze


Abstract: This paper introduces the classes $H_{\overline\Phi(n)}^{(2)}$ and $H_\Phi^{(2)}(n)$ of functions of $n$ variables. These classes, for $n=1$, are more general than the class of functions of bounded second variation introduced by F. I. Harsiladze, and in the case $n\geqslant2$ they contain the classes of functions of bounded generalized variation introduced by B. I. Golubov. Certain properties of functions of these classes are studied. A theorem on convergence and summability of Fourier series of functions from these classes is proved, and it is shown to be optimal in a certain sense.
Bibliography: 27 titles.

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English version:
Mathematics of the USSR-Sbornik, 1980, 37:2, 261–294

Bibliographic databases:

UDC: 517.512
MSC: Primary 26B30, 42B99; Secondary 42A24
Received: 20.04.1976 and 22.01.1979

Citation: T. I. Akhobadze, “Functions of bounded generalized second variation”, Mat. Sb. (N.S.), 109(151):2(6) (1979), 291–326; Math. USSR-Sb., 37:2 (1980), 261–294

Citation in format AMSBIB
\Bibitem{Akh79}
\by T.~I.~Akhobadze
\paper Functions of bounded generalized second variation
\jour Mat. Sb. (N.S.)
\yr 1979
\vol 109(151)
\issue 2(6)
\pages 291--326
\mathnet{http://mi.mathnet.ru/msb2377}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=542562}
\zmath{https://zbmath.org/?q=an:0455.42007|0417.42007}
\transl
\jour Math. USSR-Sb.
\yr 1980
\vol 37
\issue 2
\pages 261--294
\crossref{https://doi.org/10.1070/SM1980v037n02ABEH001953}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980KQ02900007}


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  • http://mi.mathnet.ru/eng/msb/v151/i2/p291

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Akhobadze T., “Continuity of Functions of Many Variables of the Generalized Bounded Variation Class”, Acta Math. Hung., 48:3-4 (1986), 317–341  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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