Monatshefte für Mathematik

, Volume 80, Issue 3, pp 171–177

On the Fourier transformation on spaces of (p,q)-multipliers

  • Bernd Dreseler
  • Walter Schempp
Article

Abstract

LetG denote a locally compact abelian topological group. The aim of the present paper is to prove an “intermediate” result between two well-known results ofL. Hörmander andG. I. Gaudry concerning the structure of the spaces ℱGℳμℓtp,q(G).

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References

  1. [1]
    Donoghue, Jr., W. F.: Distributions and Fourier Transforms. New York and London: Academic Press. 1969.Google Scholar
  2. [2]
    Edwards, R. E., andJ. F. Price: A naively constructive approach to boundedness principles, with applications to harmonic analysis. Enseignement Math.16, 255–296 (1970).Google Scholar
  3. [3]
    Gaudry, G. I.: Quasimeasures and operators commuting with convolution. Pacific J. Math.18, 461–476 (1966).Google Scholar
  4. [4]
    Gaudry, G. I.: Multipliers of type (p,q). Pacific J. Math.18, 477–488 (1966).Google Scholar
  5. [5]
    Gaudry, G. I.: Bad behavior and inclusion results for multipliers of type (p,q). Pacific J. Math.35, 83–94 (1970).Google Scholar
  6. [6]
    Hörmander, L.: Estimates for translation invariant operators inL pspaces. Acta Math.104, 93–140 (1960).Google Scholar
  7. [7]
    Larsen, R.: An Introduction to the Theory of Multipliers. Berlin-Heidelberg-New York: Springer. 1971.Google Scholar
  8. [8]
    Salem, R.: On singular monotonic functions whose spectrum has a given Hausdorff dimension. Ark. Mat.1, 353–365 (1950). Also in “Oeuvres mathématiques”, B. 34, pp. 481–493. Paris: Hermann. 1967.Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Bernd Dreseler
    • 1
  • Walter Schempp
    • 1
  1. 1.Lehrstuhl für Mathematik I der Universität SiegenSiegen 21Federal Republic of Germany

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