On Inequalities of Lieb–Thirring Type
Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 504-514
Cet article a éte moissonné depuis la source Math-Net.Ru
Applying the method proposed by Kashin for proving inequalities of Lieb–Thirring type for orthonormal systems, we prove a similar inequality in the multidimensional case.
Keywords:
Lieb–Thirring inequalities, orthogonal series, orthonormal system of functions, normalized Lebesgue measure, Rademacher system.
@article{MZM_2007_82_4_a3,
author = {D. S. Barsegyan},
title = {On {Inequalities} of {Lieb{\textendash}Thirring} {Type}},
journal = {Matemati\v{c}eskie zametki},
pages = {504--514},
year = {2007},
volume = {82},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a3/}
}
D. S. Barsegyan. On Inequalities of Lieb–Thirring Type. Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 504-514. http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a3/
[1] E. Lieb, W. Thirring, “Inequalities for the moments of the eigenvalues of the Schrödinger hamiltonian and their relation to Sobolev inequalities”, Stud. Math. Phys., Essays in Honor of Valentine Bargmann, Princeton Univ. Press, Princeton, 1976, 269–303 | Zbl
[2] A. A. Ilin, “Integralnye neravenstva Liba–Tirringa i ikh prilozheniya k attraktoram uravnenii Nave–Stoksa”, Matem. sb., 196:1 (2005), 33–66 | MR | Zbl
[3] B. S. Kashin, “Ob odnom klasse neravenstv dlya ortonormirovannykh sistem”, Matem. zametki, 80:2 (2006), 204–208 | MR | Zbl
[4] B. S. Kashin, A. A. Saakyan, Ortogonalnye ryady, AFTs, M., 1999 | MR | Zbl
[5] S. M. Nikolskii, Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977 | MR | Zbl