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

• Date: 2001
• Main Authors: Babenko, Yu. V., Бабенко, Ю. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2001
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4239
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For arbitrary t ∈ [0, 1], s ∈ [1, ∞], and A ≥ 2, we determine the unimprovable constant B for the inequality $$\left| {x\prime \left( t \right)} \right| \leqslant A\left\| x \right\|_{L_\infty \left[ {0,1} \right]} + B\left\| {x} \right\|_{L_s \left[ {0,1} \right]} .$$ .