This article is cited in 1 paper

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.

UDC: 517.538.5

MSC: 41A20, 41A25

Received: 15.12.2020
Revised: 09.04.2021
Accepted: 14.04.2021

Language: English

DOI: 10.15393/j3.art.2021.9530

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