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Probl. Anal. Issues Anal., 2021, Volume 10(28), Issue 2, Pages 54–66 (Mi pa324)  

Rational approximations of Lipschitz functions from the Hardy class on the line

M. A. Komarov

Vladimir State University, Gor'kogo street 87, Vladimir 600000, Russia

Abstract: We study a rate of uniform approximations on the real line of summable Lipschitz functions $f$ having a summable Hilbert transform $Hf$ by normalized logarithmic derivatives of rational functions. Inequalities between different metrics of the logarithmic derivatives of algebraic polynomials on the line are also considered.

Keywords: logarithmic derivative of a rational function, simple partial fraction, Hilbert transform, uniform approximation, inequality between different metrics.

DOI: https://doi.org/10.15393/j3.art.2021.9530

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Bibliographic databases:

UDC: 517.538.5
MSC: 41A20, 41A25
Received: 15.12.2020
Revised: 09.04.2021
Accepted:14.04.2021
Language:

Citation: M. A. Komarov, “Rational approximations of Lipschitz functions from the Hardy class on the line”, Probl. Anal. Issues Anal., 10(28):2 (2021), 54–66

Citation in format AMSBIB
\Bibitem{Kom21}
\by M.~A.~Komarov
\paper Rational approximations of Lipschitz functions from the Hardy class on the line
\jour Probl. Anal. Issues Anal.
\yr 2021
\vol 10(28)
\issue 2
\pages 54--66
\mathnet{http://mi.mathnet.ru/pa324}
\crossref{https://doi.org/10.15393/j3.art.2021.9530}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000661490100005}


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