Abstract
In the space L p , 1 ≤ p < 2, on the half-line with power weight, Jackson’s inequality between the value of the best approximation of a function by even entire functions of exponential type and its modulus of continuity defined by means of a generalized shift operator is well known. The question of the sharpness of the inequality remained open. For the constant in Jackson’s inequality, we obtain a lower bound, which proves its sharpness.
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Original Russian Text © V. I. Ivanov, 2015, published in Matematicheskie Zametki, 2015, Vol. 98, No. 5, pp. 684–694.
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Ivanov, V.I. On the sharpness of Jackson’s inequality in the spaces L p on the half-line with power weight. Math Notes 98, 742–751 (2015). https://doi.org/10.1134/S0001434615110048
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DOI: https://doi.org/10.1134/S0001434615110048