The space of test functions for Fourier hyperfunctions is characterized by two conditions sup |φ (x)| exp k|x|<∞ and sup|^φ (ξ) | exp h|ξ|<∞ for some h,k>0. Combining this result and the new characterization of Schwartz space in  we can easily compare two important spaces F and S which are both invariant under Fourier transformations.
Cite this article
Jaeyoung Chung, Soon-Yeong Chung, Dohan Kim, A Characterization for Fourier Hyperfunctions. Publ. Res. Inst. Math. Sci. 30 (1994), no. 2, pp. 203–208DOI 10.2977/PRIMS/1195166129