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On the Hausdorff-Young theorem for amalgams

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Abstract

Certain function spaces called amalgams have been used and studied in several recent papers on abstract harmonic analysis. In this paper, we give a new proof of a Hausdorff-Young theorem for amalgams on locally compact abelian groups. We also prove some complementary results about amalgams and their Fourier transforms, and in particular give simple proofs of some facts about the Fourier multipliers from certain spaces of functions with compact support intoA(G).

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, V6T 1Y4, Vancouver, Canada

    John J. F. Fournier

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  1. John J. F. Fournier
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Research partially suppored by N.S.E.R.C. operating grant number 4822.

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Fournier, J.J.F. On the Hausdorff-Young theorem for amalgams. Monatshefte für Mathematik 95, 117–135 (1983). https://doi.org/10.1007/BF01323655

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