Journal of the European Mathematical Society

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Volume 10, Issue 3, 2008, pp. 739–755

DOI: 10.4171/JEMS/128

Lieb–Thirring inequalities on the half-line with critical exponent

Tomas Ekholm (1) and Rupert L. Frank (2)

(1) Department of Mathematics, Royal Institute of Technology, SE-100 44, STOCKHOLM, SWEDEN
(2) Department of Mathematics, Princeton University, Fine Hall, NJ 08544, PRINCETON, UNITED STATES

We consider a Schrödinger operator on the half-line with a Dirichlet boundary condition at the origin and show that moments of its negative eigenvalues can be estimated by the part of the potential that is larger than the critical Hardy weight. The estimate is valid for the critical value of the moment parameter.

Keywords: Schrödinger operator, Lieb–Thirring inequalities, Hardy inequality