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Ukrainian Mathematical Journal

, Volume 63, Issue 9, pp 1321–1335 | Cite as

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

  • V. F. Babenko
  • M. S. Churilova
Article
  • 75 Downloads

For functions defined on the entire real axis or a semiaxis, we obtain Kolmogorov-type inequalities that estimate the L p -norms (1 ≤ p < ∞) of fractional derivatives in terms of the L p -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.

Keywords

Fractional Derivative Extremal Function Unbounded Operator Fractional Differentiation Optimal Reconstruction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  • V. F. Babenko
    • 1
  • M. S. Churilova
    • 1
  1. 1.DnepropetrovskUkraine

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