Mathematical Notes

, Volume 86, Issue 5–6, pp 753–766 | Cite as

On the possibility of strengthening the Lieb-Thirring inequality

  • D. S. Barsegyan


In 1976, Lieb and Thirring obtained an upper bound for the square of the normon L 2(ℝ2) of the sum of the squares of functions from finite orthonormal systems via the sum of the squares of the norms of their gradients. Later, a series of Lieb-Thirring inequalities for orthonormal systems was established by many authors. In the present paper, using the standard theory of functions, we prove Lieb-Thirring inequalities, which have applications in the theory of partial differential equations.

Key words

Lieb-Thirring inequality orthonormal system function theory Fourier transform partial differential equation 


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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • D. S. Barsegyan
    • 1
  1. 1.Moscow State UniversityMoscowRussia

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