Scattering theory for the Dirac equation of Hartree type and the semirelativistic Hartree equation

Consider a scattering problem for the Dirac equation with a nonlocal term including the Hartree type. We improve the condition of the potential term to show the existence of scattering operators for small initial data in the subcritical Sobolev spaces. Our proofs can be applied to the case of the semirelativistic Hartree equation, and lead to improvement of the condition of the potential.