Regularity for solutions of nonlocal parabolic equations II

We prove boundary regularity and a compactness result for parabolic nonlocal equations of the form ut−Iu=fut−Iu=f, where the operator I   is not necessarily translation invariant. As a consequence of this and the regularity results for the translation invariant case, we obtain C1,αC1,α interior estimates in space for nontranslation invariant operators under some hypothesis on the time regularity of the boundary data.