On the asymptotic estimates of the best approximations of differentiable functions by algebraić polynomials in the space $L_1$ - Motornaya, O. V. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
An asymptotically exact estimate is obtained for the best approximations of $r$ times differentiable functions by algebraic polynomials in the space $L_1$.