An asymptotically sharp estimate is obtained for the best one-sided approximation of a step by algebraic polynomials in the space L 1:
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 3, pp. 409–422, March, 2010.
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Motornyi, V.P., Motornaya, O.V. & Nitiema, P.K. One-sided approximation of a step by algebraic polynomials in the mean. Ukr Math J 62, 467–482 (2010). https://doi.org/10.1007/s11253-010-0366-y
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DOI: https://doi.org/10.1007/s11253-010-0366-y