  For projective varieties with a certain class of 'mild' isolated
singularities and for projective threefolds with arbitrary Gorenstein canonical
singularities, we show that the stringy Hodge numbers satisfy the Hard
Lefschetz property. This result fits nicely with a 6-dimensional counterexample
of Mustata and Payne for the Hard Lefschetz property for stringy Hodge numbers
in general. We also give such an example, ours is a hypersurface singularity.
