Geodesic
Approximation of functions of bounded $p$-variation by polynomials in terms of the Faber--Schauder system
Matematičeskie zametki, Tome 62 (1997) no. 3, pp. 363-371.

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In this paper the best polynomial approximation in terms of the system of Faber–Schauder functions in the space $C_p[0,1]$ is studied. The constant in the estimate of Jackson's inequality for the best approximation in the metric of $C_p[0,1]$ and the estimate of the modulus of continuity $\omega_{1-1/p}$ are refined. 
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     title = {Approximation of functions of bounded $p$-variation by polynomials in terms of the {Faber--Schauder} system},
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S. S. Volosivets. Approximation of functions of bounded $p$-variation by polynomials in terms of the Faber--Schauder system. Matematičeskie zametki, Tome 62 (1997) no. 3, pp. 363-371. http://geodesic.mathdoc.fr/item/MZM_1997_62_3_a4/

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