Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators

• Published in: Journal of the American Mathematical Society
• Main Authors: Frank, Rupert L., Lieb, Elliott H., Seiringer, Robert
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: American Mathematical Society 2007
• Subjects: Hardy inequality; relativistic Schr¨odinger operator; Lieb-Thirring inequalities; Sobolev inequalities; stability of matter; diamagnetic inequality.; laptev
• Online Access: https://doi.org/10.1090/S0894-0347-07-00582-6

We show that the Lieb-Thirring inequalities on moments of negative eigenvalues of Schrödinger-like operators remain true, with possibly different constants, when the critical Hardy-weight C │x│^(-2) is subtracted from the Laplace operator. We do so by first establishing a Sobolev inequality for...