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(∇−iA)2u−V(x)u+(λ±iϵ)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.