COORBIT DESCRIPTION AND ATOMIC DECOMPOSITION OF BESOV SPACES

Function spaces are central topics in analysis. Often those spaces and related analysis involves symmetries in form of an action of a Lie group. Coorbit theory as introduced by Feichtinger and Grochenig [6-8] and then later extended in Christensen and Olafsson [3] gives a unified method to construct Banach spaces of functions based on representations of Lie groups. In this article, we identify the homogeneous Besov spaces on stratified Lie groups introduced by Fuhr and Mayeli [12] as coorbit spaces in the sense of [3] and use this to derive atomic decompositions for the Besov spaces.