The fractional S-transform on spaces of type \(W\) (Q353033)

Restricting growths of test functions Gelfand and Shilov introduced three test function spaces, called spaces of type W, and studied continuity of Fourier transformation between these spaces. In this paper additional three suitable test function spaces are defined and continuity of fractional S-transformation [\textit{D. P. Xu} and \textit{K. Guo}, ``Fractional S transform. I: Theory, Theory Appl. Geophys. 9, No. 1, 73--79 (2012; \url{doi:10.1007/s11770-012-0316-6})] of functions belonging to spaces of type W into the corresponding spaces introduced by the present author is studied.