Lifting of Quaternionic Frames to Higher Dimensions with Partial Ridges

Abstract We consider the technique of lifting frames to higher dimensions with ridge idea that originally was introduced by Grafakos and Sansing. pursue a novel approach regard non-commutative setting, concretely skew-field quaternions. Moreover, we allow for splitting multi-ridges. To this end, introduce quaternionic Sobolev spaces prove corresponding embedding theorems. mention as concrete examples wavelet shearlet frames, give respective lifted families.