Boundedness and compactness of localization operators on the affine group

The aim of this paper is to extend some results on 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}-boundedness and compactness of localization operators, from the Weyl–Heisenberg group (Boggiatto et al. in J Math Anal Appl 322:193–206, 2006; Boggiatto and Wong in Integral Equ Oper Theory 49:1–10, 2004), giving the short-time Fourier transform, to the affine group, giving the wavelet transform.