estimates for electromagnetic Helmholtz equation

In space dimension n ⩾ 3 , we consider the electromagnetic Schrödinger hamiltonian H = ( ∇ − i A ( x ) ) 2 − V and the corresponding Helmholtz equation ( ∇ − i A ( x ) ) 2 u + u − V ( x ) u = f in R n . We extend the well-known L p – L q estimates for the solution of the free Helmholtz equation to the case when the electromagnetic hamiltonian H is considered.