## 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_
Hardy spaces on Lie groups of polynomial growth
✍ Scribed by A. F. M. ter Elst; Derek W. Robinson; YuePing Zhu
- Book ID
- 107348125
- Publisher
- SP Science China Press
- Year
- 2010
- Tongue
- English
- Weight
- 967 KB
- Volume
- 53
- Category
- Article
- ISSN
- 1674-7283
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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 Hardy spaces on homogeneous groups were introduced and studied by Folland and Stein [3]. The purpose of this note is to show that duals of Hardy spaces __H__^__p__^ , 0 < __p__ ≤ 1, on homogeneous groups can be identified with Morrey–Campanato spaces. This closes a gap in the original p