I am trying to get familiar with hyperfunctions, and I do have some familiarity with the classical theory of distributions.

**I am wondering whether hyperfunctions have any advantages over distributions. Are there any applications of the former which cannot be obtained using the latter? Any important examples?**

I was told one general property of hyperfunctions which seems to be important and which is not satisfies by usual distributions: the sheaf of hyperfunctions (on a real analytic manifold) is injective.