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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 85–95 (Mi semr1053)  

Real, complex and functional analysis

On the convergence of the Luzin integral and its analogues

K. I. Knizhova, I. V. Podviginba

a Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
b Sobolev Institute of Mathematics, 4, pr. Koptyuga, 630090, Novosibirsk, Russia

Abstract: We study the convergence at a fixed point of the singular integral of Luzin and its analogues. We present sufficient conditions in terms of the Fourier coefficients of the given integrable function for such convergence.

Keywords: trigonometric conjugate function, trigonometric conjugate series, Luzin integral.

DOI: https://doi.org/10.33048/semi.2019.16.004

Full text: PDF file (165 kB)
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Bibliographic databases:

UDC: 517.518.454, 517.518.13
MSC: 42A50
Received December 6, 2018, published January 27, 2019

Citation: K. I. Knizhov, I. V. Podvigin, “On the convergence of the Luzin integral and its analogues”, Sib. Èlektron. Mat. Izv., 16 (2019), 85–95

Citation in format AMSBIB
\Bibitem{KniPod19}
\by K.~I.~Knizhov, I.~V.~Podvigin
\paper On the convergence of the Luzin integral and its analogues
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 85--95
\mathnet{http://mi.mathnet.ru/semr1053}
\crossref{https://doi.org/10.33048/semi.2019.16.004}


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