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- Title
Estimates for the norms of fractional derivatives in terms of integral moduli of continuity and their applications.
- Authors
Babenko, V.; Churilova, M.
- Abstract
For functions defined on the entire real axis or a semiaxis, we obtain Kolmogorov-type inequalities that estimate the L-norms (1 ≤ p < ∞) of fractional derivatives in terms of the L-norms of functions (or the L-norms of their truncated derivatives) and their L-moduli of continuity and establish their sharpness for p = 1: Applications of the obtained inequalities are given.
- Subjects
FRACTIONAL calculus; MATHEMATICAL inequalities; ESTIMATION theory; MATRIX norms; INTEGRALS; MATHEMATICAL analysis
- Publication
Ukrainian Mathematical Journal, 2012, Vol 63, Issue 9, p1321
- ISSN
0041-5995
- Publication type
Article
- DOI
10.1007/s11253-012-0581-9