Geodesic
Approximation of a~Class of Singular Integrals by Algebraic Polynomials with Regard to the Location of a~Point on an Interval
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 268-285.

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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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V. P. Motornyi. Approximation of a~Class of Singular Integrals by Algebraic Polynomials with Regard to the Location of a~Point on an Interval. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 268-285. http://geodesic.mathdoc.fr/item/TM_2001_232_a21/

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