New results on the continuous Weinstein wavelet transform

We consider the continuous wavelet transform [Formula: see text] associated with the Weinstein operator. We introduce the notion of localization operators for [Formula: see text]. In particular, we prove the boundedness and compactness of localization operators associated with the continuous wavelet transform. Next, we analyze the concentration of [Formula: see text] on sets of finite measure. In particular, Benedicks-type and Donoho-Stark's uncertainty principles are given. Finally, we prove many versions of Heisenberg-type uncertainty principles for [Formula: see text].