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

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.


Hilbert Space Real Axis Unitary Operator Spectral Theory Bounded Variation 
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    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
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    L. V. Taikov, “On Hardy inequalities,” Mat. Zametki, 52, No. 4, 106–111 (1992).MathSciNetGoogle Scholar
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    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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