Abstract: Stratified Lie groups may be regarded as a noncommutative generalization of Euclidean spaces; due to the availability of operations such as shifts and dilations, many results and constructions initially studied for $mathbb{R}^n$ carry over to stratified Lie groups. One example of such a group is the Heisenberg group. Inhomogeneous Besov spaces on simply connected, connected stratified Lie groups have been studied since the late 70ies. They are usually defined in terms of the spectral measure of a sub-Laplacian acting as a replacement to the usual Laplace operator in Euclidean space. In this talk I consider the construction of the homogeneous scale of Besov-Spaces.
Outside the Euclidean setting, homogeneous Besov spaces on general stratified groups have not been studied systematically. I address questions such as independence of the choice of window function, of the choice of sub-Laplacian, and characterizations via continuous and fully discrete wavelet systems.
(Joint work with Azita Mayeli.)