On Lieb-Thirring inequalities for Schrodinger operators with virtual level

We consider the operator H = - Delta- V in L-2(R-d), d >= 3. For the moments of its negative eigenvalues we prove the estimate tr H--(gamma) <= C-gamma,C-d integral(Rd) (V(x) - (d-2)(2)/4\x\(2))(gamma+d/2) dx, gamma > 0. Similar estimates hold for the one-dimensional operator with a Dirichlet condition at the origin and for the two-dimensional Aharonov-Bohm operator.