Coorbit description and atomic decomposition of Besov spaces

TL;DR

This paper identifies homogeneous Besov spaces on stratified Lie groups as coorbit spaces, providing a unified framework and deriving atomic decompositions for these function spaces using group representations.

Contribution

It extends coorbit theory to include Besov spaces on stratified Lie groups, offering a new perspective and tools for analysis of these spaces.

Findings

Homogeneous Besov spaces are characterized as coorbit spaces.

Atomic decompositions for Besov spaces are derived.

The framework unifies analysis of Besov spaces via Lie group representations.

Abstract

Function spaces are central topic 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 Gr\"ochenig and then later extended in [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 in [13] as coorbit spaces in the sense of [3] and use this to derive atomic decompositions for the Besov spaces.