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 wordsinequality of Lieb-Thirring type orthonormal system orthogonal series classical Littlewood-Paley theorem Cauchy’s inequality
Unable to display preview. Download preview PDF.
- 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.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
- 5.S. M. Nikol’skii, Approximation of Functions of Several Variables and Embedding Theorems [in Russian], Fizmatlit, Moscow, 1977.Google Scholar
© Springer Science+Business Media, Inc. 2006