Hostname: page-component-84b7d79bbc-dwq4g Total loading time: 0 Render date: 2024-07-28T10:38:57.235Z Has data issue: false hasContentIssue false
  • English
  • Français

The Norm of the Lp-Fourier Transform, II

Published online by Cambridge University Press:  20 November 2018

Bernard Russo
Bernard Russo*
Affiliation:
University of California, Irvine, California
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let G be a locally compact separable unimodular group. The general theory [18] assigns to G a measure space (Λ, μ) whose points ƛ index a family of unitary factor representations of G in such a way that if U ƛ corresponds to ƛ and then

for all .

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 6 , 01 December 1976 , pp. 1121 - 1131
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Auslander, L. and Kostant, B., Polarization and unitary representations of solvable Lie groups, Invent. Math. 14 (1971), 255–354.Google Scholar
2. Babenko, K. I., On an inequality in the theory of Fourier integrals, Izv. Akad. Nauk SSSR, Ser. Mat. 25 (1961), 531–542 (Russian).Google Scholar
3. Dixmier, J., Sur les representations unitaires des groupes de Lie nilpotents, I, Amer. J. Math. 10 (1958), 160-170. IL Bull. Soc. Math. France 85 (1957), 325-388. III. Can. J. Math. 10 (1958), 321-348. IV. Can. J. Math. 11 (1959), 321-344. V. Bull. Soc. Math. France 87 (1959), 65-79. VI. Can. J. Math. 12 (1960), 342–352.Google Scholar
4. Dixmier, J., Les C*-algebres et leur representations (Gauthier-Villars, Paris, 1964, Second Edition, 1969).Google Scholar
5. Keene, F. W., Square integrable representations of Iwasawa subgroups of a semi-simple Lie group, Thesis, University of California, Berkeley, 1974.Google Scholar
6. Kirillov, A. A., Unitary representations of nilpotent Lie groups, Uspekhi Matem. Nauk 106 (1962), 57–110 (Russian).Google Scholar
7. Kleppner, A. and Lipsman, R., The Plancher el formula for group extensions, I, Ann. Scient. Ec. Norm. Sup., 4th series, 5 (1972), 459-516. II, same journal, 6 (1973), 103–132.Google Scholar
8. Kunze, R. A., Lp Fourier transforms on locally compact unimodular groups, Trans. Amer. Math. Soc. 89 (1958), 519–540.Google Scholar
9. Lipsman, R. L., Non-abelian Fourier analysis, Bull. Sci. Math. 98 (1974), 209–233.Google Scholar
10. Fournier, J. J. F., Sharpness in the Hausdorff Young theorem on unimodular groups, Notices Amer. Math. Soc. 22 (1975), A-486.Google Scholar
11. M∞re, C. C., Representations of solvable and nilpotent groups and harmonic analysis on nil and solvmanifolds, 1972 Summer Institute on Harmonic Analysis on Homogeneous spaces, A.M.S.Google Scholar
12. M∞re, C. C. and Wolf, J. A., Square integrable representations of nilpotent groups, Trans. Amer. Math. Soc. 185 (1973), 445–462.Google Scholar
13. Naimark, M. A., Linear representations of the Lorentz group, (Macmillan, 1964).Google Scholar
14. Pukanszky, L., Leçons sur les representations des groups (Dunod, 1967).Google Scholar
15. Pukanszky, L., Unitary representations of solvable Lie groups, Ann. scient. Ec. Norm. Sup., 4th series, 4 (1971), 457–608.Google Scholar
16. Quint, S. R., Representations of Lie groups, Lecture notes, University of California, Berkeley, 1972.Google Scholar
17. Russo, B., The norm of theLp-Fourier transform on unimodular groups, Trans. Amer. Math. Soc. 192 (1974), 293–305.Google Scholar
17a. Russo, B., On the Hausdorff Young theorem for integral operators, to appear, Pacific J. Math.Google Scholar
18. Segal, I. E., An extension of PlanchereVs formula to separable unimodular groups, Ann. of Math. 5 (1950), 272–292.Google Scholar
19. Warner, G., Harmonic analysis on semisimple Lie groups I, II (Springer Verlag, 1972).Google Scholar