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 Tr. Mat. Inst. Steklova, 2001, Volume 232, Pages 268–285 (Mi tm218)

Approximation of a Class of Singular Integrals by Algebraic Polynomials with Regard to the Location of a Point on an Interval

V. P. Motornyi

Dnepropetrovsk State University

Abstract: A pointwise approximation of singular integrals $S(f)(x)=\frac 1\pi \int _{-1}^1\frac {f(t)}{t-x}\frac 1{\sqrt {1-t^2}} dt$, $x\in (-1,1)$, of functions from the class $W^rH^{\omega }$ by algebraic polynomials is analyzed ($\omega(t)$ is a convex upward modulus of continuity such that $t\omega '(t)$ is a nondecreasing function). The estimates obtained cannot be improved simultaneously for all moduli of continuity.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2001, 232, 260–277

Bibliographic databases:
UDC: 517.5

Citation: V. P. Motornyi, “Approximation of a Class of Singular Integrals by Algebraic Polynomials with Regard to the Location of a Point on an Interval”, Function spaces, harmonic analysis, and differential equations, Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii, Tr. Mat. Inst. Steklova, 232, Nauka, MAIK «Nauka/Inteperiodika», M., 2001, 268–285; Proc. Steklov Inst. Math., 232 (2001), 260–277

Citation in format AMSBIB
\Bibitem{Mot01} \by V.~P.~Motornyi \paper Approximation of a~Class of Singular Integrals by Algebraic Polynomials with Regard to the Location of a~Point on an Interval \inbook Function spaces, harmonic analysis, and differential equations \bookinfo Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii \serial Tr. Mat. Inst. Steklova \yr 2001 \vol 232 \pages 268--285 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm218} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1851454} \zmath{https://zbmath.org/?q=an:1005.41002} \transl \jour Proc. Steklov Inst. Math. \yr 2001 \vol 232 \pages 260--277 

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This publication is cited in the following articles:
1. T. S. Mardvilko, A. A. Pekarskii, “Conjugate Functions on the Closed Interval and Their Relationship with Uniform Rational and Piecewise Polynomial Approximations”, Math. Notes, 99:2 (2016), 272–283
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