Bojanov – Naidenov problem for the differentiable functions on the real line and the inequalities of various metrics

• Datum: 2019
• Hauptverfasser: Kofanov, V. A., Кофанов, В. А.
• Format: Artikel
• Sprache: Russisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2019
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/1476
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 For given $r \in {\rm \bf N},$ $p,\lambda > 0$ and any fixed interval $[a, b]\subset {\rm \bf R}$ we solve the extremal problem $$ \int\limits_{a}^{b} |x(t)|^q dt \to \sup, \quad q\ge p, $$ on a set of functions $x\in L^r_{\infty}$ such that $$ \|x^{(r)}\|_{\infty} \le 1,\quad \|x...