Estimates for the norms of fractional derivatives in terms of integral moduli of continuity and their applications

• Date: 2011
• Main Authors: Babenko, V. F., Churilova, M. S., Бабенко, В. Ф., Чурилова, М. С.
• 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/2794
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For functions defined on the real line or a half-line, we obtain Kolmogorov-type inequalities that estimate the $L_p$-norms $(1 \leq p < \infty)$ of fractional derivatives in terms of the Lp-norms of functions (or the $L_p$-norms of their truncated derivatives) and their $L_p$-moduli of conti...