LP multipliers on noncompact symmetric spaces

Journal fur die Reine und Angewandte Mathematik

Volumn 1997, Issue 482, 1997, Pages 151-176

  Giulini, Saverio ^a   Mauceri, Giancarlo ^a   Meda, Stefano ^a  

^a NONE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21444446470     PISSN: 00754102     EISSN: 14355345     Source Type: Journal    
DOI: 10.1515/crll.1997.482.151     Document Type: Article

References (22)

1. J.-Ph. Anker, Sharp estimates for some functions of the Laplacian on noncompact symmetric spaces Duke Math. J. 65 (1992), 257-297.
2. J.-Ph. Anker, LP Fourier multipliers on Riemannian symmetric spaces of the noncompact type Ann. Math. 132 (1990), 597-628.
3. J.-P. Anker and N. Lohouè, Multiplicateurs sur certains espaces symétriques Amer. J. Math. 108 (1986), 1303-1354.
4. A. Baernstein II and T. Sawyer, Embedding and multiplier theorems for Hp(R”) Mem. Amer. Math. Soc. 318 (1985), 1-82.
5. J.L. Clerc, Transformation de Fourier sphérique des espaces de Schwartz J. Funet. Anal. 37 (1980), 182-202.
6. J.L. Clerc and E.M. Stein, Lp multipliers for noncompact symmetric spaces Proc. Nat. Acad. Sci U.S.A. 71 (1974), 3911-3912.
7. M.G. Cowling, Harmonic analysis on semigroups Ann. Math. 117 (1983), 267-283.
8. M.G. Cowling, S. Giulini and S. Meda, LP - Lq estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. I Duke Math. J. 72 (1993), 109-150.
9. M.G. Cowling, S. Giulini and S. Meda, LP - Lq estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. Ill preprint.
10. P. Eymard, Algèbres Ap et convoluteurs de Lp. Sem. Bourbaki 367, November 1969.
11. A. Figà-Talamanca and M. Picardello, Harmonic Analysis on Free Groups. Lect. Notes Pure Appi. Math. 87, Marcel Dekker, 1983.
12. R. Gangolli, On the Plancherel formula and the Paley-Wiener theorem for spherical functions on semisimple Lie groups Ann. Math. 93 (1971), 150-165.
13. P. Graczyk and J.-J. Loeby Bochner and Schoenberg theorems on symmetric spaces in the complex case Bull. Soc. Math. France 122 (1994), 571-590.
14. S. Helgason, Groups and Geometric Analysis Academic Press, New York 1984.
15. C.S. Herz, Le rapport entre l'algèbre Ap d'un groupe et d'un sous-groupe C. R. Acad. Sc. Paris 271 (1970), 244-246.
16. L. Hörmander, Estimates for translation invariant operators in LP spaces Acta Math. 104 (1960), 93-140.
17. L. Hörmander, The Analysis of Linear Partial Differential Operators. Vol. I, Springer Verlag, Berlin 1983.
18. C. Meaney, Transferring estimates for zonal convolution operators Anal. Math. 15 (1989), 175-193.
19. R.J. Stanton and P.A. Tomas, Expansions for spherical functions on noncompact symmetric spaces Acta Math. 140 (1978), 251-276.
20. E.M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidan Spaces Princeton University Press, Princeton N.J. 1971.
21. M. Taylor, IP estimates on functions of the Laplace operator Duke Math. J. 58 (1989), 773-793.
22. G.N. Watson, A Treatise on the Theory of Bessel Functions Cambridge Univ. Press, London 1962.