Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-19T23:44:09.951Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimates for kernels of intertwining operators on SL(n, R)

Part of: Harmonic analysis in several variables Lie groups

Published online by Cambridge University Press:  09 April 2009

Michael Cowling  and
Stefano Meda
Michael Cowling
Affiliation:
School of Mathematics, University of New South Wales, UNSW Sydney, NSW 2052, Australia, e-mail: M.Cowling@unsw.edu.au
Stefano Meda
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via Bicocca degli Arcimboldi 8, 20126 Milano, Italy, e-mail: stefano.meda@unimib.it
Rights & Permissions [Opens in a new window]

Abstract

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.

In this paper we study the kernels and the Lp–Lq boundedness properties of some intertwining operators associated to representations of SL(n, R).

Keywords

semisimple Lie groupsintertwining operatorsmultiparameter potential operators.

MSC classification

Secondary: 22E30: Analysis on real and complex Lie groups 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 81 , Issue 1 , August 2006 , pp. 105 - 120
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Cowling, M., ‘Herz' “principe de majoration” and the Kunze-Stein phenomenon’, CMS Conf. Proc. 21 (1997), 73–88.Google Scholar
[2]Gindikin, S. and Karpelevič, S., ‘Plancherel measure of Riemannian symmetric spaces of nonpositive curvature’, Dokl. Akad. Nauk SSSR 145 (1962), 252–255.Google Scholar
[3]Helgason, S., Differential geometry, Lie groups and symmetric spaces (Academic Press, New York, 1978).Google Scholar
[4]Hörmander, L., ‘Estimates for translation invariant operators in Lp spaces’, Acta Math. 104 (1960), 93–140.CrossRefGoogle Scholar
[5]Hunt, R. A., ‘On L(p, q) spaces’, Enseign. Mat. 12 (1956), 249–276.Google Scholar
[6]Knapp, A. W., Representation theory of semisimple Lie groups (Princeton University Press. Princeton, 1986).CrossRefGoogle Scholar
[7]Knapp, A. W. and Stein, E. M., ‘Intertwining operators on semisimple Lie groups’, Ann. of Math. (2) 93 (1971), 489–578.CrossRefGoogle Scholar
[8]Kunze, R. A. and Stein, E. M., ‘Uniformly bounded representations and harmonic analysis of the 2 x 2 real unimodular group’, Amer. J. Math. 82 (1960), 1–62.CrossRefGoogle Scholar
[9]Kunze, R. A. and Stein, E. M., ‘Uniformly bounded representations II. Analytic continuation of the principal series of representations of the n x n complex unimodular group’, Amer. J. Math. 83 (1961), 723–786.CrossRefGoogle Scholar
[10]Kunze, R. A. and Stein, E. M., ‘Uniformly bounded representations III. Intertwining operators for the principal series on semisimple groups’, Amer. J. Math. 89 (1967), 385–442.CrossRefGoogle Scholar
[11]Schiffmann, G., ‘Intégrales d'entrelacement et fonctions de Whittaker’, Bull. Soc. Math. France 99 (1971), 3–72.CrossRefGoogle Scholar