Non-trapping magnetic fields and Morrey–Campanato estimates for Schrödinger operators

We prove some uniform in ϵ a priori estimates for solutions of the equation ( ∇ − i A ) 2 u − V ( x ) u + ( λ ± i ϵ ) u = f , λ ⩾ 0 , ϵ ≠ 0 . The estimates are obtained in terms of Morrey–Campanato norms, and can be used to prove absence of zero-resonances, in a suitable sense, for electromagnetic Hamiltonians. Quantitative conditions on the size of the trapping component of the magnetic field and the non-repulsive component of the electric field are given.