Estimates for the norms of fractional derivatives in terms of integral moduli of continuity and their applications

  • V. F. Babenko
  • M. S. Churilova Днепропетр. нац. ун-т


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.
How to Cite
Babenko, V. F., and M. S. Churilova. “Estimates for the Norms of Fractional Derivatives in Terms of Integral Moduli of Continuity and Their Applications”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 9, Sept. 2011, pp. 1155-68,
Research articles