Uniform resolvent estimates for critical magnetic Schrödinger operators in 2D

Abstract

We study the $L^p-L^q$-type uniform resolvent estimates for 2D-Schrödinger operators in scaling-critical magnetic fields, involving the Aharonov-Bohm model as a main example. As an application, we prove localization estimates for the eigenvalue of some non self-adjoint zero-order perturbations of the magnetic Hamiltonian.

31 pages. We add some remarks after Theorem 1.2 and correct some typos in the new version. Comments are welcome!