### Abstract

We show that the Lieb-Thirring inequality on moments of negative eigenvalues remains true, with a possibly different constant, when the critical Hardy-weight is subtracted from the Laplace operator. A similar statement is true for fractional powers of the Laplacian, in particular relativistic Schr\"odinger operators.

The talk is based on joint works with T. Ekholm and with E. Lieb and R. Seiringer.