Coorbit spaces associated to integrably admissible dilation groups

This paper considers coorbit spaces parametrized by mixed, weighted Lebesgue with respect to the quasi-regular representation of semi-direct product Euclidean space and a suitable matrix dilation group. The class groups that we allow, so-called integrably admissible groups, contains yielding an irreducible, square-integrable as proper subclass. obtained scale extends therefore well-studied wavelet associated discrete series representations. We show for any group there exists convienent smooth, analyzing vectors can be used define consistent possessing all essential properties are known hold in setting In particular, realized Besov-type decomposition means Littlewood—Paley-type characterization. classes anisotropic Besov expansive matrices shown coincide precisely induced one-parameter groups.