Pointwise bounds on eigenstates in non-relativistic QED

In the present paper, Kato's distributional inequality with magnetic field is generalized to vector-valued functions and operator-valued vector potentials. This result is then used in non-relativistic quantum electrodynamics (QED) to show that eigenstates of the Pauli-Fierz Hamiltonian satisfy a subsolution estimate, and hence that any $L^2$-exponential bound in terms of a Lipschitz function implies the corresponding pointwise exponential bound. Similar pointwise bounds are also established for the one-particle density of states that are not eigenstates.