Geodesic
On the best $L_1$-approximation by algebraic polynomials to truncated powers and to classes of functions with $L_1$-bounded derivative
Izvestiya. Mathematics , Tome 63 (1999) no. 3, pp. 561-582.

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We establish the asymptotic behaviour of the best $L_1$-approximations of the kernels $(x-a)_+^{r-1}$, $r>2$ and the corresponding classes $W_1^r$ by algebraic polynomials. 
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V. P. Motornyi; O. V. Motornaya. On the best $L_1$-approximation by algebraic polynomials to truncated powers and to classes of functions with $L_1$-bounded derivative. Izvestiya. Mathematics , Tome 63 (1999) no. 3, pp. 561-582. http://geodesic.mathdoc.fr/item/IM2_1999_63_3_a5/

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