Abstract
The problem of the asymmetric ideal spline least deviating from zero in theC[a,b]-metric is solved. On this basis, the Landau-Kolmogorov-Hörmander inequalities for the norms of positive and negative parts of intermediate derivatives of functions of the semiaxis that take into account restrictions on the positive and negative part of the higher derivative are proved. Thus, the well-known Shönberg-Cavaretta inequality is generalized and refined.
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Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 175–185, February, 1999.
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Babenko, V.F., Kofanov, V.A. & Pichugov, S.A. Landau-kolmogorov-hörmander inequalities on the semiaxis. Math Notes 65, 144–152 (1999). https://doi.org/10.1007/BF02679810
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DOI: https://doi.org/10.1007/BF02679810