Geodesic
Estimates for the error of approximation of classes of differentiable functions by Faber--Schauder partial sums
Sbornik. Mathematics, Tome 197 (2006) no. 3, pp. 303-314

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In the metric of the space $\varphi(L)$ generated by a continuous even function $\varphi(x)$ increasing on $[0,\infty)$ such that $\varphi(0)=0$, $\lim_{x\to\infty}\varphi(x)=\infty$ one finds estimates of the error of approximation by partial sums of Faber–Schauder series in the function classes $C^1$ and $W^1H_\omega$, where $\omega(t)$ is a concave modulus of continuity. Bibliography: 21 titles. 
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     author = {S. B. Vakarchuk and A. N. Shchitov},
     title = {Estimates for the error of approximation of classes of differentiable functions by {Faber--Schauder} partial sums},
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S. B. Vakarchuk; A. N. Shchitov. Estimates for the error of approximation of classes of differentiable functions by Faber--Schauder partial sums. Sbornik. Mathematics, Tome 197 (2006) no. 3, pp. 303-314. http://geodesic.mathdoc.fr/item/SM_2006_197_3_a0/