We establish subsolution estimates for vector-valued Sobolev functions obeying a very mild subharmonicity condition. Our results generalize and improve a well-known subsolution estimate in the scalar-valued case, and, most importantly, they apply to models from non-relativistic quantum field theory: for eigenstates of the Nelson and Pauli-Fierz models we show that an L2-exponential bound in terms of a Lipschitz function implies the corresponding pointwise exponential bound. This is joint work with M. Griesemer.
