Time-frequency concentration and localization operators associated with the directional short-time fourier transform

In the present article, we prove new quantitative uncertainty principles for the directional short-time Fourier transform. Next, we introduce the notion of the generalized wavelet multipliers associated with the inverse of the directional short-time Fourier transform. We study the boundedness, Schatten class properties of these operator and give a trace formula. In particular we prove that the generalized Landau-Pollak-Slepian operator is a generalized wavelet multiplier. Finally, we investigate the boundedness and compactness of the generalized wavelet multipliers in the Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{p}$$\end{document}-spaces.