Resolvent Estimates for Schrödinger Operators with Potentials in Lebesgue Spaces

Abstract

We prove resolvent estimates in the Euclidean setting for Schrödinger operators with potentials in Lebesgue spaces: $-\Delta +V$. The $(L^2,L^p)$ estimates were already obtained by Blair-Sire-Sogge, but we extend their result to other $(L^p,L^q)$ estimates using their idea and the result and method of Kwon-Lee on non-uniform resolvent estimates in the Euclidean space.

16 pages, 2 figures