## Abstract Let (𝒳, __d__,__μ__) be a space of homogeneous type in the sense of Coifman and Weiss. Assuming that __μ__ satisfies certain estimates from below and there exists a suitable Calderón reproducing formula in __L__ ^2^(𝒳), the authors establish a Lusin‐area characterization for the atomic
On a Littlewood-Paley Identity and Characterization of Wavelets
✍ Scribed by C.K. Chui; X.L. Shi
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 459 KB
- Volume
- 177
- Category
- Article
- ISSN
- 0022-247X
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## 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_
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