Boundedness and compactness of localization operators on the affine group

Abstract

The aim of this paper is to extend some results on the Lp-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.