TY - JOUR
AU - O. Kozynenko
AU - D. Skorokhodov
PY - 2020/10/25
Y2 - 2022/09/27
TI - Kolmogorov type inequalities for norms of fractional derivatives of functions defined on the positive half-line
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 72
IS - 10
SE - Research articles
DO - 10.37863/umzh.v72i10.1074
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1074
AB - UDC 517.5We 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 addition, we solve the following related problems: the Stechkin problem on the best approximation of the operator $D^k_-$ by linear bounded operators and the problem on the best recovery of the operator $D^k_-$ by using a class of elements given with an error.
ER -