The paper under review introduces a generalization of I. Daubechies’ localization operators [IEEE Trans. Inf. Theory 34, No. 4, 605–612 (1988; Zbl 0672.42007)], by means of introducing the dependence of the operator on an additional Weyl-Heisenberg wavelet. The main results provide sufficient conditions for such generalizations to be bounded and compact operators on the spaces \(L^p(\mathbb{R}^d)\), where \(p \in [r, r']\), with special interest given to the case \(1\leq p \leq \infty\).