Publications and Research
Document Type
Article
Publication Date
2012
Abstract
We establish wavelet characterizations of homogeneous Besov spaces on stratified Lie groups, bothin terms of continuous and discrete wavelet systems. We first introduce a notion of homogeneous Besov space ̇Bsp,qin terms of a Littlewood-Paley-type decomposition, in analogy to the well-known characterization of the Euclidean case. Such decompositions can be defined via the spectral measure of a suitably chosen sub-Laplacian. We prove that the scale of Besov spaces is independent of the precise choice of Littlewood-Paley decomposition. In particular, different sub-Laplacians yield the same Besov spaces. We then turn to wavelet characterizations, first via continuous wavelet transforms which can be viewed as continuous-scale Littlewood-Paley decompositions, then via discretely indexed systems. We prove the existence of wavelet frames and associate datomic decomposition formulas for all homogeneous Besov spaces ̇Bsp,q with 1≤p, q <∞ands R.
Comments
This article was originally published in the Journal of Function Spaces and Applications, available at http://dx.doi.org/10.1155/2012/523586.
This work was distributed under the terms of the Creative Commons Attribution 3.0 Unported (CC BY 3.0) License.