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. 
@article{IM2_1999_63_3_a5,
     author = {V. P. Motornyi and O. V. Motornaya},
     title = {On the best $L_1$-approximation by algebraic polynomials to truncated powers and to classes of functions with $L_1$-bounded derivative},
     journal = {Izvestiya. Mathematics },
     pages = {561--582},
     publisher = {mathdoc},
     volume = {63},
     number = {3},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1999_63_3_a5/}
}
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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/