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Generalized Amalgams, With Applications to Fourier Transform

Published online by Cambridge University Press:  20 November 2018

Hans G. Feichtinger
Hans G. Feichtinger*
Affiliation:
Department of Mathematics University of Maryland College Park, MD, 20742 USA
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A recent survey article by J. Fournier and J. Stewart (Bull.AMS 13 (1985), 1-21) explains how amalgams of Lp with lq (as function spaces over any locally compact abelian group G) can be used as an effective tool for the treatment of various problems in harmonic analysis. The present article may be seen as a complement to this survey, indicating further advantages that arise if one works with generalized amalgams (introduced in 1980 under the name of Wiener-type spaces by the author [10]). The main difference between amalgams and these more general spaces is the fact that they allow a more precise description of the local behavior of functions (or distributions) by rather arbitrary norms and that the conditions on the global behavior (of the quantity obtained using that chosen local norm) is described in a way that includes both growth and integrability conditions (not only lq-summability).

Keywords

46E3043A1543A25generalized amalgams(generalized) Fourier transformcomplex interpolationWiener type spacesHausdorff-Young inequalityp-localizableultra-distributions
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 3 , 01 June 1990 , pp. 395 - 409
Copyright
Copyright © Canadian Mathematical Society 1990

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