Inequalities for derivatives of functions in the spaces Lp

• Datum: 2008
• Hauptverfasser: Kofanov, V. A., Кофанов, В. А.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2008
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3248
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

The following sharp inequality for local norms of functions $x \in L^{r}_{\infty,\infty}(\textbf{R})$ is proved: $$\frac1{b-a}\int\limits_a^b|x'(t)|^qdt \leq \frac1{\pi}\int\limits_0^{\pi}|\varphi_{r-1}(t)|^q dt \left(\frac{||x||_{L_{\infty}(\textbf{R})}}{||\varphi_r||_{\infty}}\right)^{\f...