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

Abstract

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.
Published
25.09.2011
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, https://umj.imath.kiev.ua/index.php/umj/article/view/2794.
Section
Research articles