  We consider magnetic Schr\"odinger operators describing a quantum Hall effect
setup both in the plane and in the half-plane. First, we study the structure
and smoothness of the operator range of various powers of the half-plane
resolvent. Second, we provide a complete analysis of the diamagnetic current
density at positive temperature: we prove that bulk and edge current densities
are smooth functions and we show that the edge current density converges to the
bulk current density faster than any polynomial in the inverse distance from
the boundary. Our proofs are based on gauge covariant magnetic perturbation
theory and on a detailed analysis of the integral kernels of functions of
magnetic Schr\"odinger operators on the half-plane.
