Geodesic
Asymptotics of the approximation of continuous and differentiable functions by the singular integrals of de la Vall\'ee Poussin
Matematičeskie zametki, Tome 21 (1977) no. 6, pp. 769-776.

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The complete asymptotic developments in powers of $1/n$ are derived for quantities characterizing approximation by singular integrals of de la Vallée Poussin \begin{gather*} V_n(f;x)=\frac1{\Delta_n}\int_{-\pi}^\pi f(x+t)\cos^{2n}\frac t2\,dt; \\ \Delta_n=\int_{-\pi}^\pi\cos^{2n}\frac t2\,dt \end{gather*} of the function classes $\operatorname{Lip}\alpha$, $0\alpha\le1$, $W^{(r)}$, $r\ge1$ an integer. 
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     author = {V. A. Baskakov},
     title = {Asymptotics of the approximation of continuous and differentiable functions by the singular integrals of de la {Vall\'ee} {Poussin}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {769--776},
     publisher = {mathdoc},
     volume = {21},
     number = {6},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_6_a3/}
}
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V. A. Baskakov. Asymptotics of the approximation of continuous and differentiable functions by the singular integrals of de la Vall\'ee Poussin. Matematičeskie zametki, Tome 21 (1977) no. 6, pp. 769-776. http://geodesic.mathdoc.fr/item/MZM_1977_21_6_a3/