$L^p$ resolvent estimates for magnetic Schrödinger operators with unbounded background fields

Abstract

We prove $L^p$ and smoothing estimates for the resolvent of magnetic Schrödinger operators. We allow electromagnetic potentials that are small perturbations of a smooth, but possibly unbounded background potential. As an application, we prove an estimate on the location of eigenvalues of magnetic Schrödinger and Pauli operators with complex electromagnetic potentials.

24 pages

References in corpus (2)

• Smoothing - Strichartz Estimates for the Schrodinger Equation with small Magnetic Potential
• Remark on the Kato smoothing effect for Schrödinger equation with superquadratic potentials