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Ukrainian Mathematical Journal

, Volume 61, Issue 10, pp 1533–1540 | Cite as

Refinement of a Hardy–Littlewood–Pólya-type inequality for powers of self-adjoint operators in a Hilbert space

  • V. F. Babenko
  • R. O. Bilichenko
Article
  • 34 Downloads

The well-known Taikov’s refined versions of the Hardy – Littlewood – Pólya inequality for the L 2 -norms of intermediate derivatives of a function defined on the real axis are generalized to the case of powers of self-adjoint operators in a Hilbert space.

Keywords

Hilbert Space Real Axis Unitary Operator Spectral Theory Bounded Variation 
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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References

  1. 1.
    G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge University, Cambridge (1934).Google Scholar
  2. 2.
    V. F. Babenko, N. P. Korneichuk, V. A. Kofanov, and S. A. Pichugov, Inequalities for Derivatives and Their Applications [in Russian], Naukova Dumka, Kiev (2003).Google Scholar
  3. 3.
    L. V. Taikov, “Refinement of a Hardy inequality that contains an estimate for the value of the intermediate derivative of a function,” Mat. Zametki, 50, No. 4, 114–122 (1991).MathSciNetGoogle Scholar
  4. 4.
    L. V. Taikov, “On Hardy inequalities,” Mat. Zametki, 52, No. 4, 106–111 (1992).MathSciNetGoogle Scholar
  5. 5.
    N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in a Hilbert Space [in Russian], Nauka, Moscow (1966).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  • V. F. Babenko
    • 1
    • 2
  • R. O. Bilichenko
    • 1
  1. 1.Dnepropetrovsk National UniversityDnepropetrovskUkraine
  2. 2.Institute of Applied Mathematics and MechanicsUkrainian National Academy of SciencesDonetskUkraine

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