Directional short-time Fourier transform of distributions

In this paper we consider the directional short-time Fourier transform (DSTFT) that was introduced and investigated in (Giv in J. Math. Anal. Appl. 399:100-107, 2013). We analyze the DSTFT and its transpose on test function spaces S(Rn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {S}(\mathbb {R}^{n})$\end{document} and S(Y2n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {S}(\mathbb {Y}^{2n})$\end{document}, respectively, and prove the continuity theorems on these spaces. Then the obtained results are used to extend the DSTFT to spaces of distributions.