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Pointwise Inequalities of Landau–Kolmogorov Type for Functions Defined on a Finite Segment

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Abstract

For arbitrary t ∈ [0, 1], s ∈ [1, ∞], and A ≥ 2, we determine the unimprovable constant B for the inequality

$$\left| {x\prime \left( t \right)} \right| \leqslant A\left\| x \right\|_{L_\infty \left[ {0,1} \right]} + B\left\| {x} \right\|_{L_s \left[ {0,1} \right]} .$$

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  1. Dnepropetrovsk University, Dnepropetrovsk

    Yu. V. Babenko

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  1. Yu. V. Babenko
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Babenko, Y.V. Pointwise Inequalities of Landau–Kolmogorov Type for Functions Defined on a Finite Segment. Ukrainian Mathematical Journal 53, 270–275 (2001). https://doi.org/10.1023/A:1010469004645

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