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On multipliers of Fourier transforms

Published online by Cambridge University Press:  24 October 2008

Louis Pigno
Louis Pigno
Affiliation:
Kansas State University
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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

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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