  In this manuscript we prove the Bernstein inequality and develop the theory
of holonomic D-modules for rings of invariants of finite groups in
characteristic zero, and for strongly F-regular finitely generated graded
algebras with FFRT in prime characteristic. In each of these cases, the ring
itself, its localizations, and its local cohomology modules are holonomic. We
also show that holonomic D-modules, in this context, have finite length. We
obtain these results using a more general version of Bernstein filtrations.
