Skip to main content
SpringerLink
Log in

Lieb-Thirring inequality for L p norms

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

In this paper, we obtain the Lieb-Thirring inequality for L p -norms. The proof uses only the standard apparatus of the theory of orthogonal series.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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 (Princeton Univ. Press, Princeton, NJ, 1976), pp. 269–303.

    Google Scholar 

  2. R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, in Applied Mathematical Sciences (Springer-Verlag, New York, 1997), Vol. 68.

    Google Scholar 

  3. A. A. Il’in, “Lieb-Thirring integral inequalities and their applications to attractors of Navier-Stokes equations,” Mat. Sb. 196(1), 33–66 (2005) [Russian Acad. Sci. Sb.Math. 196 (1), 29–61 (2005)].

    MathSciNet  Google Scholar 

  4. B. S. Kashin, “On a class of inequalities for orthonormal systems,” Mat. Zametki 80(2), 204–208 (2006) [Math. Notes 80 (1–2), 199–203 (2006)].

    MathSciNet  Google Scholar 

  5. J.-M. Ghidaglia, M. Marion, and R. Temam, “Generalization of the Sobolev-Lieb-Thirring inequalities and applications to the dimension of attractors,” Differential Integral Equations 1(1), 1–21 (1988).

    MATH  MathSciNet  Google Scholar 

  6. A. Eden and C. Foias, “A simple proof of the generalized Lieb-Thirring inequalities in one-space dimension,” J. Math. Anal. Appl. 162(1), 250–254 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  7. B. S. Kashin and A. A. Saakyan, Orthogonal Series (AFTs, Moscow, 1999) [in Russian].

    Google Scholar 

  8. S. M. Nikol’skii, Approximation of Functions of Several Variables and Embedding Theorems (Nauka, Moscow, 1969) [in Russian].

    Google Scholar 

  9. I. Stein, Singular Integrals and Differentiability Properties of Functions (Princeton University Press, Princeton, NJ, 1970; Mir, Moscow, 1973).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Samara State University, Samara, Russia

    S. V. Astashkin

Authors
  1. S. V. Astashkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. V. Astashkin.

Additional information

Original Russian Text © S. V. Astashkin, 2008, published in Matematicheskie Zametki, 2008, Vol. 83, No. 2, pp. 163–169.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Astashkin, S.V. Lieb-Thirring inequality for L p norms. Math Notes 83, 145–151 (2008). https://doi.org/10.1134/S0001434608010173

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434608010173

Key words

Search

Navigation