Asymptotic results for some generalized integral transforms

The extension of integral transforms to generalized function spaces and their asymptotic analysis is an important рesearch subject, that took attention on different authors. So, first we give a brief summary about some generalized asymptotics and make a short review of known results for integral transforms which are already extended on distribution spaces and their asymptotics. Then on more detailed manner, we provide the results about the extension of the directional short-time Fourier transform and Stockwell transform on the space of distributions, and we give several Abelian and Tauberian type results for these transforms