Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T01:05:27.218Z Has data issue: false hasContentIssue false
  • English
  • Français

On multipliers of Fourier transforms

Published online by Cambridge University Press:  24 October 2008

Louis Pigno
Louis Pigno
Affiliation:
Kansas State University
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper G is a locally compact Abelian group, φ a complex-valued function defined on the dual Γ, Lp(G) (1 ≤ p ≤ ∞) the usual Lebesgue space of index p formed with respect to Haar measure, C(G) the set of all bounded continuous complex-valued functions on G, and C0(G) the set of all f ∈ C(G) which vanish at infinity.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 1 , January 1972 , pp. 63 - 66
Copyright
Copyright © Cambridge Philosophical Society 1972

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Doss, R.On the multiplicators of some classes of Fourier transforms. Proc. London Math. Soc. (2) 50 (1949), 169–195.Google Scholar
(2)Edwards, D. A.On translates of L ∞-functions. J. London Math. Soc. 36 (1961), 431–432.CrossRefGoogle Scholar
(3)Edwards, R. E.Fourier series, A modern introduction, vol. II. Holt, Rinehart and Winston (New York, 1967).Google Scholar
(4)Edwards, R. E.On factor functions. Pacific J. Math. 5 (1955), 367–378.CrossRefGoogle Scholar
(5)Hewitt, E. and Ross, K. A.Abstract harmonic analysis, vol. I (Springer-Verlag; Heidelberg and New York, 1963).Google Scholar
(6)Hewitt, E. and Ross, K. A.Abstract harmonic analysis, vol. I (Springer-Verlag; Heidelberg and New York, 1970).Google Scholar
(7)Hormander, L.Estimates for translation invariant operators in L ν spaces. Acta Math. 104 (1960), 93–140.CrossRefGoogle Scholar
(8)Pigno, L.A multiplier theorem. Pacific J. Math. 34 (1970), 755–757.CrossRefGoogle Scholar
(9)Rudin, W.Fourier analysis on groups (Interscience; New York, 1962).Google Scholar
(10)Verblunsky, S.On some classes of Fourier series. Proc. London Math. Soc. (2) 33 (1932), 287–327.CrossRefGoogle Scholar
(11)Zygmund, A.Remarque sur un théorème de M. Fekete. Bull. Acad. Polonaise Sci. Lett. (1927), 343–347.Google Scholar