Dispersive estimates and absence of embedded eigenvalues

In [2] Kenig, Ruiz and Sogge proved ‖u‖ L 2n n−2 (Rn) . ‖Lu‖ L 2n n+2 (Rn) provided n ≥ 3, u ∈ C∞ 0 (Rn) and L is a second order operator with constant coefficients such that the second order coefficients are real and nonsingular. As a consequence of [3] we state local versions of this inequality for operators with C2 coefficients. In this paper we show how to apply these local versions to the absence of embedded eigenvalues for potentials in L n+1 2 and variants thereof.