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A homomorphism theorem for multipliers

Published online by Cambridge University Press:  20 January 2009

Nakhlé Habib Asmar
Affiliation:
Department of Mathematics and Computer Science, California State University, Long Beach, Long, Beach, California 90840, USA
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Throughout the paper, the symbols G1 and G2 will denote two locally compact abelian groups with character groups X1 and X2, respectively. Haar measures on Gj are denoted by μj; the ones on Xj are denoted by θj (j=1,2). The measures μj and θj are normalized so that the Plancherel Theorem holds (see [7, p. 226, Theorem 31.18]).

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

REFERENCES

1.Asmar, Nakhlé and Hewitt, Edwin, Riesz's, Marcel theorem on conjugate Fourier series and its descendants, Proceedings of the analysis conference, held in Singapore June 1986 (North-Holland, to appear).Google Scholar
2.Berkson, Earl and Gillespie, T. A., The generalized M. Riesz theorem and transference, Pacific J. Math. 120 (2) (1985), 279288.CrossRefGoogle Scholar
3.Berkson, Earl, Gillespie, T. A. and Muhly, Paul, Generalized analyticity in UMD spaces, Ark. Mat., to appear.Google Scholar
4.Coifman, Ronald and Weiss, Guido, Transference methods in analysis, Regional conference series in Math. 31 (Amer. Math. Soc., Providence, 1977).Google Scholar
5.Edwards, R. E. and Gaudry, G. I., Littlewood-Paley and multiplier theory (Berlin,Heidelberg, New York: Springer-Verlag, 1977).CrossRefGoogle Scholar
6.Hewitt, Edwin and Ross, Kenneth, Abstract Harmonic Analysis I, SecondEdition (Berlin,Heidelberg, New York: Springer-Verlag, 1979).CrossRefGoogle Scholar
7.Hewitt, Edwin and Ross, Kenneth, Abstract Harmonic Analysis II, (Berlin, Heidelberg, New York: Springer-Verlag, 1970).Google Scholar
8.Deleeuw, Karel, On Lp multipliers, Ann. of Math. 81 (1965), 364379.CrossRefGoogle Scholar
9.Saeki, Sadahiro, Translation invariant operators on groups, Tohoku Math. J. 22 (1970), 409419.CrossRefGoogle Scholar