Now 6 and rjt are open, hence r] is open. Then ' p is open because i, and i, are topological. c]
Groups of Polynomial Growth and Their Associated Metric Spaces
โ Scribed by F. Point
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 711 KB
- Volume
- 175
- Category
- Article
- ISSN
- 0021-8693
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๐ SIMILAR VOLUMES
## Abstract We introduce a LittlewoodโPaley decomposition related to any subโLaplacian on a Lie group __G__ of polynomial volume growth; this allows us to prove a LittlewoodโPaley theorem in this general setting and to provide a dyadic characterization of Besov spaces __B__ ^__s,q__^ ~__p__~ (__G_
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.