A simple and consistent definition of homogeneous Besov spaces on stratified Lie groups

Abstract

We introduce a general definition of homogeneous Besov spaces on a stratified Lie group $G$, based on a Littlewood-Paley-type decomposition of Schwartz functions with all moments vanishing. We show that under mild and intuitive conditions the spaces thus defined are independent of the decomposition employed. A corollary of this is that previously constructed versions of homogeneous Besov spaces on $G$, relying on the spectral calculus of a sub-Laplacian of the group, are consistent, i.e., independent of the choice of sub-Laplacian. We further prove characterizations of homogeneous Besov spaces using continuous wavelet transforms, with a large variety of analysing wavelets to choose from.

arXiv comment13 pages. This paper has not been submitted. It has been merged with the paper arXiv:1007.4041, which has appeared in the meantime