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Examples of Coorbit Spaces for Dual Pairs

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Abstract

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.

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Authors and Affiliations

  1. Department of mathematics, Louisiana State University, 329 Lockett Hall, Baton Rouge, LA, USA

    Jens Gerlach Christensen & Gestur Ólafsson

Authors
  1. Jens Gerlach Christensen
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  2. Gestur Ólafsson
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Correspondence to Jens Gerlach Christensen.

Additional information

J.G. Christensen gratefully acknowledges support from the Louisiana Board of Regents under grant LEQSF(2005-2007)-ENH-TR-21 and NSF grant DMS-0801010.

The research of G. Ólafsson was supported by NSF grants DMS-0402068 and DMS-0801010.

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Christensen, J.G., Ólafsson, G. Examples of Coorbit Spaces for Dual Pairs. Acta Appl Math 107, 25–48 (2009). https://doi.org/10.1007/s10440-008-9390-4

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