  In this work we study microlocal regularity of hyperfunctions defining in
this context a class of generalized FBI transforms first introduced for
distributions by Berhanu and Hounie. Using a microlocal decomposition of a
hyperfunction and the generalized FBI transforms we were able to characterize
the wave-front set of hyperfunctions according several types of regularity. The
microlocal decomposition allowed us to recover and generalize both classical
and recent results and, in particular, we proved for differential operators
with real-analytic coefficients that if the elliptic regularity theorem
regarding any reasonable regularity holds for distributions, then it is
automatically true for hyperfunctions.

Analysis of PDEs