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

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Ukrainian Mathematical Journal Aims and scope

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.

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Authors and Affiliations

  1. Dnepropetrovsk National University, Dnepropetrovsk, Ukraine

    V. F. Babenko & M. S. Churilova

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  1. V. F. Babenko
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  2. M. S. Churilova
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 9, pp. 1155–1168, September, 2011.

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Babenko, V.F., Churilova, M.S. Estimates for the norms of fractional derivatives in terms of integral moduli of continuity and their applications. Ukr Math J 63, 1321–1335 (2012). https://doi.org/10.1007/s11253-012-0581-9

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  • DOI: https://doi.org/10.1007/s11253-012-0581-9

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