Centered densities on Lie groups of polynomial volume growth
✍ Scribed by Georgios K. Alexopoulos
- Publisher
- Springer
- Year
- 2002
- Tongue
- English
- Weight
- 288 KB
- Volume
- 124
- Category
- Article
- ISSN
- 1432-2064
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📜 SIMILAR VOLUMES
Let G be a Lie group of polynomial growth. We prove that the second-order Riesz transforms on L 2 (G ; dg) are bounded if, and only if, the group is a direct product of a compact group and a nilpotent group, in which case the transforms of all orders are bounded.
## Abstract We introduce a Littlewood–Paley decomposition related to any sub‐Laplacian on a Lie group __G__ of polynomial volume growth; this allows us to prove a Littlewood–Paley theorem in this general setting and to provide a dyadic characterization of Besov spaces __B__ ^__s,q__^ ~__p__~ (__G_