In this paper, we define and study the continuous wavelet transform \(\Phi _{h}\) associated with the Poly-axially operator. We prove for this transform a new Plancherel’s formula, inversion theorem. Moreover, we study the extremal functions associated to the multidimensional Fourier–Bessel transform. Next, we define and study the two-wavelet localization operator, also we investigate the localization operators for \(\Phi _{h}\) in particular we prove that they are in the Schatten-von Neumann class.
