2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57932We derive Lieb-Thirring inequalities for the Riesz means of eigenvalues of order gamma >= 3/4 for fourth order Schrödinger operators in arbitrary dimensions. We also consider some extensions to polyharmonic operators, and to systems of such operators. For the critical case gamma = 1 - 1/2l in dimension d=1 with differential order 2l >= 4 we prove the strict inequality L^0(l,gamma,d) < L(l,gamma,d), which holds in contrast to current conjectures.18 pages, submitted to Comm. Part. Diff. EqMathematical PhysicsSpectral Theory35P15 (Primary) 47A75, 35J10 (Secondary)text