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Mat. Sb. (N.S.), 1976, Volume 99(141), Number 1, Pages 84–120 (Mi msb2707)  

This article is cited in 3 scientific papers (total in 3 papers)

A generalized integral and conjugate functions

I. A. Vinogradova


Abstract: The author gives a descriptive definition of the $LG^*$-integral. The $LG^*$-integral extends the Lebesgue integral and coincides with it for nonnegative functions. For a function $f(x)$, $LG^*$-integrable on $[0,2\pi]$, the $LG^*$-Fourier series is defined and is almost everywhere $(C,1)$ summable to $f(x)$; the conjugate series is $(C,1)$ summable to $\widetilde f(x)$, which is also $LG^*$-integrable on $[0,2\pi]$, and is its $LG^*$-Fourier series.
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Sbornik, 1976, 28:1, 73–106

Bibliographic databases:

UDC: 517.397
MSC: Primary 42A40; Secondary 26A39
Received: 10.04.1975

Citation: I. A. Vinogradova, “A generalized integral and conjugate functions”, Mat. Sb. (N.S.), 99(141):1 (1976), 84–120; Math. USSR-Sb., 28:1 (1976), 73–106

Citation in format AMSBIB
\Bibitem{Vin76}
\by I.~A.~Vinogradova
\paper A~generalized integral and conjugate functions
\jour Mat. Sb. (N.S.)
\yr 1976
\vol 99(141)
\issue 1
\pages 84--120
\mathnet{http://mi.mathnet.ru/msb2707}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=402394}
\zmath{https://zbmath.org/?q=an:0332.42012}
\transl
\jour Math. USSR-Sb.
\yr 1976
\vol 28
\issue 1
\pages 73--106
\crossref{https://doi.org/10.1070/SM1976v028n01ABEH001641}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1976EM69000005}


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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. R. A. Aliyev, “Representability of Analytic Functions in Terms of Their Boundary Values”, Math. Notes, 73:1 (2003), 8–20  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. T. P. Lukashenko, “The $A$-integral and its application in the investigations of P.  L. Ul'yanov and other mathematicians”, Russian Math. (Iz. VUZ), 52:5 (2008), 67–71  mathnet  crossref  mathscinet  zmath
    3. R. A. Aliyev, “$N^\pm$-integrals and boundary values of Cauchy-type integrals of finite measures”, Sb. Math., 205:7 (2014), 913–935  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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