Ultradistribution is an element of the space $\mathcal{Z}'$ dual to the space $\mathcal{Z}$ of test functions whose Fourier transform is in the space $\mathcal{D}$ of infinitely differentiable functions of compact support.
Related $n$Lab pages include distribution
• Morisuke Hasumi, Note on the $n$-tempered ultra-distributions, Tohoku Math. J. (2) 13 (1961), no. 1, 94–104 doi euclid