Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-11T05:06:22.346Z Has data issue: false hasContentIssue false

Sur les Transformées de Riesz sur les Groupes de Lie Moyennables et sur Certains Espaces Homogènes

Published online by Cambridge University Press:  20 November 2018

Noël Lohoué
Affiliation:
Mathématiques, Bât. 425, UniversitéParis XI, Orsay 91405 Cedex.France
Sami Mustapha
Affiliation:
Institut de Mathématiques, UniversitéParis VI 4, place Jussieu Paris 75252 Cedex, France
Rights & Permissions [Opens in a new window]

Abstract

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1998

References

1. Alexopoulos, G., An application of homogenization theory to harmonic analysis: Harnack inequalities and Riesz transforms on Lie groups of polynomial growth. Canad. J. Math. 44(1992), 691727.Google Scholar
2. Anker, J.-P., Damek, E. et Yacoub, C., Spherical analysis on harmonic AN groups (àparaître).Google Scholar
3. Coifman, R.R. et Weiss, G., Analyse harmonique non commutative sur certains espaces homogènes. Lectures Notes in Math. 242, Springer-Verlag, 1971.Google Scholar
4. Eymard, P., Moyennes Invariantes et Représentations Unitaires. Lecture Notes in Math. 300, Springer- Verlag, 1972.Google Scholar
5. Gaudry, G., Qian, T. et Sögren, P., Singular integrals related to the Laplacian on the group ax + b. Ark. Mat. 30(1992), 259281.Google Scholar
6. Lipsman, R., Uniformly bounded representations of. SL2(C). Amer. J. Math. 91(1969), 4766.Google Scholar
7. Lohoué, N., Transformées de Riesz et fonctions de Littlewood Paley sur les groupes non moyennables. C. R. Acad. Sci. Paris Sér. I Math. 306(1988), 327330.Google Scholar
8. Lohoué, N., Estimations Lp des coefficients de représentation et opérateurs de convolution. Adv. Math. 38(1980), 178221.Google Scholar
9. Lohoué, N., Analyse sur les espaces homogènes des groupes non-moyennables (àparâıtre).Google Scholar
10. Lohoué, N., Transformées de Riesz et fonctions sommables. Amer. J.Math. (4) 114(1992), 327330.Google Scholar
11. Lohoué, N. et Varopoulos, N. Th., Remarques sur les transformées de Riesz sur les groupes de Lie nilpotents. C. R. Acad. Sci. Paris Sér. I Math. 301(1985), 559560.Google Scholar
12. Saloff-Coste, L., Analyse sur les groupes de Lie à croissance polynômiale. Ark.Mat. 28(1990), 315331.Google Scholar
13. Sögren, P., An estimate for a first-order Riesz operator on the affine group. Preprint.Google Scholar
14. Rieter, H., Classical Harmonic Analysis and Locally CompactGroups. Oxford Math.Monographs, 1968.Google Scholar
15. Robinson, D.W., Elliptic Operators and Lie Groups. Oxford Math. Monographs, 1991.Google Scholar
16. Varopoulos, N. Th., The heat kernel on Lie groups. Rev. Mat. Iberoamericana 12(1996), 147186.Google Scholar
17. Varopoulos, N. Th., Diffusions on Lie groups (II). Canad. J. Math. 46(1994), 1073.ndash;1093.Google Scholar
18. Varopoulos, N. Th., Sallof-Coste, L. et Coulhon, Th., Analysis and Geometry on Groups. Cambridge Tracts in Math. 100(1993).Google Scholar
19. Varopoulos, N. Th., Small time Gaussian estimates of heat diffusion kernels (I), The semi-group technique. Bull. Sci. Math. Sér. II 113(1989), 253277.Google Scholar
20. Zygmund, A., Trigonometric series. Vol. I et II, 2e édition, Cambridge Univ. Press, 1959.Google Scholar