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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 2, Pages 399–421 (Mi izv2254)  

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

The asymptotic $L_p$-norm of differentiated Fourier sums of functions of bounded variation

B. I. Golubov


Abstract: An asymptotic expression as $n\to\infty$ is found for the norms $\|S_n^{(r)}(x,f)\|_{L_q}$ ($1\le p<q<\infty$, $r=1,2,…$), where $S_n(x,f)$ is a Fourier sum of the $2\pi$-periodic function $f(x)$ having bounded $p$-variation. Various criteria for the continuity of a function of bounded $p$-variation are obtained as corollaries.

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:2, 401–423

Bibliographic databases:

UDC: 517.5
MSC: Primary 42A16, 26A45; Secondary 26A15
Received: 22.09.1971

Citation: B. I. Golubov, “The asymptotic $L_p$-norm of differentiated Fourier sums of functions of bounded variation”, Izv. Akad. Nauk SSSR Ser. Mat., 37:2 (1973), 399–421; Math. USSR-Izv., 7:2 (1973), 401–423

Citation in format AMSBIB
\Bibitem{Gol73}
\by B.~I.~Golubov
\paper The asymptotic $L_p$-norm of differentiated Fourier sums of functions of bounded variation
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 2
\pages 399--421
\mathnet{http://mi.mathnet.ru/izv2254}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=364989}
\zmath{https://zbmath.org/?q=an:0264.42003}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 2
\pages 401--423
\crossref{https://doi.org/10.1070/IM1973v007n02ABEH001945}


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    This publication is cited in the following articles:
    1. M. S. Bespalov, “Explicit form of the Dirichlet kernel for Walsh series and transformations”, Sb. Math., 196:7 (2005), 935–957  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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