Geodesic
On the Possibility of Strengthening the Lieb--Thirring Inequality
Matematičeskie zametki, Tome 86 (2009) no. 6, pp. 803-818.

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In 1976, Lieb and Thirring obtained an upper bound for the square of the norm on $L^2(\mathbb R^2)$ 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.
Keywords: Lieb–Thirring inequality, orthonormal system, function theory, partial differential equation.
Mots-clés : Fourier transform 
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D. S. Barsegyan. On the Possibility of Strengthening the Lieb--Thirring Inequality. Matematičeskie zametki, Tome 86 (2009) no. 6, pp. 803-818. http://geodesic.mathdoc.fr/item/MZM_2009_86_6_a0/

[1] E. H. Lieb, W. Thirring, “Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities”, Studies in Mathematical Physics. Essays in Honor of Valentine Bargmann, Princeton Univ. Press, Princeton, NJ, 1976, 269–303 | Zbl

[2] B. S. Kashin, “Ob odnom klasse neravenstv dlya ortonormirovannykh sistem”, Matem. zametki, 80:2 (2006), 204–208 | MR | Zbl

[3] D. S. Barsegyan, “O neravenstvakh tipa Liba–Tirringa”, Matem. zametki, 82:4 (2007), 504–514 | MR | Zbl

[4] S. V. Astashkin, “Neravenstvo Liba–Tirringa dlya $L_p$-norm”, Matem. zametki, 83:2 (2008), 163–169 | MR | Zbl

[5] B. C. Kashin, A. A. Saakyan, Ortogonalnye ryady, Izd-vo AFTs, M., 1999 | MR | Zbl

[6] S. M. Nikolskii, Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977 | MR | Zbl

[7] I. P. Natanson, Teoriya funktsii veschestvennoi peremennoi, Nauka, M., 1974 | MR | Zbl