The paper generalizes a few results of \textit{M. A. Solov'ev} [Theor. Math. Phys. 15, 317-328 (1974; Zbl 0273.46030)] and adds further results in line with the first author's work on the subject. The Fourier-Laplace transform of functionals defined on the spaces \(Sa^q_k\) are considered. It may be mentioned here that \textit{J. M. C. Joshi} has considered generalized Fourier, Laplace, and Stieltjes transforms (called S. M. Joshi generalized Fourier, Laplace, and Stieltjes transforms) of generalized functions. He has considered cones and tube domains. For complete bibliography the following may be seen: ``Recent studies in distributional integral transforms in fractional calculus and its applications'' (K. Nishimoto ed.), Proc. Int. Conf. Tokyo 1989, 59-61 (1990; Zbl 0862.46022); ``Recent studies in integral transforms'', Indian Journal of Natural and Physical Sciences, Gurukul Kangri (Hardwar) (1997).