Geodesic
Rational approximations of Lipschitz functions from the Hardy class on the line
Problemy analiza, Tome 10 (2021) no. 2, pp. 54-66

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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, uniform approximation, inequality between different metrics.
Mots-clés : Hilbert transform 
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     author = {M. A. Komarov},
     title = {Rational approximations of {Lipschitz} functions from the {Hardy} class on the line},
     journal = {Problemy analiza},
     pages = {54--66},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2021_10_2_a4/}
}
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M. A. Komarov. Rational approximations of Lipschitz functions from the Hardy class on the line. Problemy analiza, Tome 10 (2021) no. 2, pp. 54-66. http://geodesic.mathdoc.fr/item/PA_2021_10_2_a4/