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 to 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.

在这项工作中，我们研究了超函数的微局部正则性，在这种情况下，它定义了由Berhanu和Hounie首次引入分布的一类广义FBI变换。使用超函数的微局部分解和广义的FBI变换，我们能够根据几种规律性来表征超函数的波前集合。微观局部分解使我们能够恢复和推广经典和最近的结果，特别是，我们针对具有实解析系数的微分算子证明，如果关于任何合理正则性的椭圆正则定理对分布成立，那么对超函数而言它自动成立。