Estimates for the norms of fractional derivatives in terms of integral moduli of continuity and their applications - Babenko, V. F.; Churilova, M. S. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
For functions defined on the real line or a half-line, we obtain Kolmogorov-type inequalities that estimate the L_p-norms (1 ≤ p < ∞) 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.