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Multipliers for Amalgams and the Algebra S0(G)

Published online by Cambridge University Press:  20 November 2018

Maria L. Torres De Squire
Maria L. Torres De Squire*
Affiliation:
University of Regina, Regina, Saskatchewan
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Throughout the whole paper G will be a locally compact abelian group with Haar measure m and dual group Ĝ. The difference of two sets A and B will be denoted by A ∼ B, i.e.,

For a function f on G and s ∊ G, the functions f′ and fs will be defined by

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 1 , 01 February 1987 , pp. 123 - 148
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Bertrandias, J. P. and Dupuis, C., Transformation de Fourier su les espaces lp(Lp′), Ann. Inst. Fourier, Grenoble 29 (1979), 189–206.Google Scholar
2. Bertrandias, J. P., Datry, C. and Dupuis, C., Unions et intersections d'espaces Lp invariantes par translation ou convolution, Ann. Inst. Fourier, Grenoble. 28 (1978), 53–84.Google Scholar
3. Bertrandias, J. P., Espaces lp(A) et l∞(Q), (to appear).Google Scholar
4. Burnham, J. T. and Goldberg, R. R., Multipliers from L1(G) to a Segal algebra, Bull. Inst. Math. Acad. Sinica. 2 (1974), 153–164.Google Scholar
5. Busby, R. C. and Smith, H. A., Product-convolution operators and mixed-norm spaces, Trans. Am. Math. Soc. 263 (1981), 309–341.Google Scholar
6. Cowling, M., Some applications of Grothendieck's theory of topological tensor products in harmonic analysis, Math. Ann. 232 (1978), 273–285.Google Scholar
7. Doran, R. S. and Wichmann, J., Approximate identities and factorization in Banach modules 768, (Springer-Verlag, 1970).Google Scholar
8. Edwards, R. E., On factor functions, Pac. J. Math. 5 (1955), 367–378.Google Scholar
9. Feichtinger, H. G., Multipliers from L1(G) to a homogeneous Banach space, J. Math. Anal. Appl. 61 (1977), 341–356.Google Scholar
10. Feichtinger, H. G., Un espace de Banach de distributions tempérées sur les groupes localement compact abeliens, C.R. Acad. Sci. Paris. 290 (1980), 791–794.Google Scholar
11. Feichtinger, H. G., On a new Segal algebra, Mh. Math. 92 (1981), 269–289.Google Scholar
12. Gaudry, G. I., Quasimeasures and operators commuting with convolution, Pac. J. Math. 18 (1966), 461–476.Google Scholar
13. Gaudry, G. I., Multipliers of type (p, q), Pac. J. Math. 18 (1966), 477–488.Google Scholar
14. Gaudry, G. I., Topics in harmonic analysis, Lecture Notes (Department of Mathematics, Yale University, New Haven, Ct., 1969).Google Scholar
15. Hewitt, E. and Ross, K. A., Abstract harmonic analysis I, II, (Springer-Verlag, 1970, 1979).CrossRefGoogle Scholar
16. Holland, F., Harmonic analysis on amalgams of Lp and Lq , J. London Math. Soc. (2) 10 (1975), 295–305.Google Scholar
17. Kelly, J. L., Namioka, I. and coauthors., Linear topological spaces, (Princeton, N.J., D. van Nostrand, 1963).CrossRefGoogle Scholar
18. Liu, T., van Rooij, A. and Wang, J., On some group algebras of modules related to Wiener's algebra M1 , Pac. J. Math. 55 (1974), 507–520.Google Scholar
19. Losert, V., A characterization of the minimal strongly character invariant Segal algebra, Ann. Inst. Fourier, Grenoble 30 (1980), 129–139.Google Scholar
20. Reiter, H., L1-algebras and Segal algebras, 231 (Springer-Verlag, 1971).CrossRefGoogle Scholar
21. Stewart, J., Fourier transforms of unbounded measures, Can. J. Math. 31 (1979), 1281–1292.Google Scholar
22. Torres de Squire, M. L., Amalgams of Lp and lq , Ph. D. Thesis, McMaster University (1984).Google Scholar