Jean Dolbeault, Ari Laptev, and Michael Loss
Lieb-Thirring inequalities with improved constants
(15K, LaTeX)

ABSTRACT.  Following Eden and Foias we obtain a matrix version of a generalised Sobolev inequality in one-dimension. This allow us to improve on the known estimates of best constants in Lieb-Thirring inequalities for the sum of the negative eigenvalues for multi-dimensional Schroedinger operators.