Mathematical Notes

, Volume 80, Issue 1–2, pp 199–203 | Cite as

On a class of inequalities for orthonormal systems

  • B. S. Kashin


In this paper, a novel approach to the proof of inequalities of Lieb-Thirring type based on the standard apparatus of the theory of orthogonal series is proposed.

Key words

inequality of Lieb-Thirring type orthonormal system orthogonal series classical Littlewood-Paley theorem Cauchy’s inequality 


  1. 1.
    E. Lieb and W. Thirring, “Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities,” in: Studies in Mathematical Physics, Essays in honor of Valentine Bargmann, Princeton Univ. Press, Princeton, 1976, pp. 269–303.Google Scholar
  2. 2.
    A. A. Il’in, “Integral Lieb-Thirring inequalities and their applications to the attractors of Navier-Stokes equations,” Mat. Sb. [Russian Acad. Sci. Sb. Math.], 196 (2005), no. 1, 33–66.Google Scholar
  3. 3.
    R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, 1997.MATHGoogle Scholar
  4. 4.
    B. S. Kashin and A. A. Sahakian, Orthogonal Series [in Russian], AFTs, Moscow, 1999.MATHGoogle Scholar
  5. 5.
    S. M. Nikol’skii, Approximation of Functions of Several Variables and Embedding Theorems [in Russian], Fizmatlit, Moscow, 1977.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • B. S. Kashin
    • 1
  1. 1.V. A. Steklov Mathematics InstituteRussian Academy of SciencesRussia

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