Acta Applicandae Mathematicae

, Volume 107, Issue 1–3, pp 25–48 | Cite as

Examples of Coorbit Spaces for Dual Pairs

  • Jens Gerlach ChristensenEmail author
  • Gestur Ólafsson


In this paper we summarize and give examples of a generalization of the coorbit space theory initiated in the 1980’s by H.G. Feichtinger and K.H. Gröchenig. Coorbit theory has been a powerful tool in characterizing Banach spaces of distributions with the use of integrable representations of locally compact groups. Examples are a wavelet characterization of the Besov spaces and a characterization of some Bergman spaces by the discrete series representation of SL2(ℝ). We present examples of Banach spaces which could not be covered by the previous theory, and we also provide atomic decompositions for an example related to a non-integrable representation.


Coorbit spaces Gelfand triples Representation theory of locally compact groups 

Mathematics Subject Classification (2000)

43A15 42B35 22D12 


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© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of mathematicsLouisiana State UniversityBaton RougeUSA

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