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 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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.zbMATHGoogle Scholar
  4. 4.
    B. S. Kashin and A. A. Sahakian, Orthogonal Series [in Russian], AFTs, Moscow, 1999.zbMATHGoogle 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

Personalised recommendations