Estimates for the norms of fractional derivatives in terms of integral moduli of continuity and their applications
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 continuity and establish their sharpness for $p = 1$. Applications of the obtained inequalities are given.
English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 9, pp 1321-1335.
Citation Example: Babenko V. F., Churilova M. S. Estimates for the norms of fractional derivatives in terms of integral moduli of continuity and their applications // Ukr. Mat. Zh. - 2011. - 63, № 9. - pp. 1155-1168.