Sharp upper bounds of norms of functions and their derivatives on classes of functions with given comparison function

• Date: 2011
• Main Authors: Kofanov, V. A., Кофанов, В. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2011
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2778
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For arbitrary $[\alpha, \beta] \subset \textbf{R}$ and $p > 0$, we solve the extremal problem $$\int_{\alpha}^{\beta}|x^{(k)}(t)|^q dt \rightarrow \sup, \quad q \geq p, \quad k = 0, \quad \text{or} \quad q \geq 1, \quad k \geq 1,$$ on the set of functions $S^k_{\varphi}$ such that$\varphi...