Following Eden and Foias we obtain a matrix version of a generalised Sobolev inequality in one-dimension. This allows us to improve on the known estimates of best constants in Lieb-Thirring inequalities for the sum of the negative eigenvalues for multi-dimensional Schrödinger operators.
Cite this article
Ari Laptev, Jean Dolbeault, Michael Loss, Lieb–Thirring inequalities with improved constants. J. Eur. Math. Soc. 10 (2008), no. 4, pp. 1121–1126DOI 10.4171/JEMS/142