Kolmogorov type inequalities for norms of fractional derivatives of functions defined on the positive half-line

• Date: 2020
• Main Authors: Kozynenko, O., Skorokhodov, D., Козиненко, Александр, Скороходов, Дмитро, Козиненко, О., Скороходов, Д.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2020
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1074
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 We obtain new Kolmogorov type sharp inequalities that estimate the norm of the Marchaud fractional derivative $\big\|D^k_-f\big\|_\infty$ of a function $f$ defined on the positive half-line in terms of $\|f\|_p,$ $1< p<\infty,$ and $\|f''\|_1.$ In ad...