Kolmogorov type inequalities for norms of fractional derivatives of functions defined on the positive half-line - Kozynenko, O.; Skorokhodov, D.; Козиненко, Александр; Скороходов, Дмитро; Козиненко, О.; Скороходов, Д. (Institute of Mathematics, NAS of Ukraine, 2020)
UDC 517.5 We obtain new Kolmogorov type sharp inequalities that estimate the norm of the Marchaud fractional derivative $\big\|D^k_-f\big\|_∞$ of a function $f$ defined on the positive half-line in terms of $\|f\|_p,$ $1< p<∞,$ 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.