LpLp–LqLq estimates for electromagnetic Helmholtz equation

In space dimension n⩾3n⩾3, we consider the electromagnetic Schrödinger hamiltonian H=(∇−iA(x))2−VH=(∇−iA(x))2−V and the corresponding Helmholtz equation(∇−iA(x))2u+u−V(x)u=fin Rn. We extend the well-known LpLp–LqLq estimates for the solution of the free Helmholtz equation to the case when the electromagnetic hamiltonian H is considered.